There is a colony of villains with several holes aligned in a row, where each hole contains exactly one villain.Each colony arrangement can be expressed as a string of even length, where the $$$i$$$-th character of the string represents the type of villain in the $$$i$$$-th hole. Iron Man can destroy a colony only if the colony arrangement is such that all villains of a certain type either live in the first half of the colony or in the second half of the colony.His assistant Jarvis has a special power. It can swap villains of any two holes, i.e. swap any two characters in the string; he can do this operation any number of times.Now Iron Man asks Jarvis $$$q$$$ questions. In each question, he gives Jarvis two numbers $$$x$$$ and $$$y$$$. Jarvis has to tell Iron Man the number of distinct colony arrangements he can create from the original one using his powers such that all villains having the same type as those originally living in $$$x$$$-th hole or $$$y$$$-th hole live in the same half and the Iron Man can destroy that colony arrangement.Two colony arrangements are considered to be different if there exists a hole such that different types of villains are present in that hole in the arrangements.

The first line contains a string $$$s$$$ ($$$2 \le |s| \le 10^{5}$$$), representing the initial colony arrangement. String $$$s$$$ can have both lowercase and uppercase English letters and its length is even. The second line contains a single integer $$$q$$$ ($$$1 \le q \le 10^{5}$$$) — the number of questions. The $$$i$$$-th of the next $$$q$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le |s|$$$, $$$x_i \ne y_i$$$) — the two numbers given to the Jarvis for the $$$i$$$-th question.

For each question output the number of arrangements possible modulo $$$10^9+7$$$.

NoteConsider the first example. For the first question, the possible arrangements are "aabb" and "bbaa", and for the second question, index $$$1$$$ contains 'a' and index $$$2$$$ contains 'b' and there is no valid arrangement in which all 'a' and 'b' are in the same half.

var s = readline();
var qq = readline().split(" ").map(function(x) { return parseInt(x); })[0];

var cnt = Array(52).fill(0);

const ALPHABET = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';
get_ind = function (c) {
 	return ALPHABET.indexOf(c);
};

const MOD = 1000000007;

mulmod = function(a, b) {
  if (a < b) a = b + (b=a, 0);   // swap
  var x = 0, y = a % MOD;
  while (b) {
    if (b & 1) {
    	x += y;
    	if (x >= MOD) x -= MOD;
    }
    y <<= 1;
    if (y >= MOD) y -= MOD;
    b >>= 1;
  }
  return x;
}

find_deg = function(x, deg) {
	var b = 1, a = x % MOD;
	while (deg) {
		if (deg & 1) b = mulmod(b, a);
		deg >>= 1;
		if (deg > 0) a = mulmod(a, a);
	}
	return b % MOD;
};

find_rev = function(x) {
	return find_deg(x, MOD-2);   // MOD is prime, so MOD-2 is correct Phi-1 value
};

var fakt = Array(s.length+1).fill(0);
var rev_fakt = Array(s.length+1).fill(0);

cnk = function(n, k) {
	return mulmod(mulmod(fakt[n], rev_fakt[k]), rev_fakt[n-k]);
}

var half = Math.floor(s.length / 2);
var dp = Array(half + 1).fill(0);

solve = function(wth) {
	var sum_wth = 0;
	for (var i=0; i<wth.length; i++) sum_wth += cnt[wth[i]];
	if (sum_wth > half)
		return 0;

	var dp_copy = dp.slice();
	for (var i=0; i<wth.length; i++)
		for (var j=0; j+cnt[wth[i]] <= half; j++)
			if (dp_copy[j] > 0)
				dp_copy[j+cnt[wth[i]]] = (dp_copy[j+cnt[wth[i]]] - dp_copy[j] + MOD) % MOD;

	return dp_copy[half];
}

for (var i=0; i<s.length; i++)
	cnt[get_ind(s[i])]++;

var ans = 0;

var inv = Array(s.length+1).fill(0);
inv[1] = 1;
for (var i=2; i<=s.length; i++) inv[i] = mulmod(inv[MOD % i], (MOD - Math.floor(MOD/i)));
fakt[0] = 1; fakt[1] = 1;
rev_fakt[0] = 1; rev_fakt[1] = 1;
for (var i=2; i<=s.length; i++) {
	fakt[i] = mulmod(fakt[i-1],i);
	rev_fakt[i] = mulmod(rev_fakt[i-1], inv[i]);
}

var glob_rev = 1;
for (var i=0; i<52; i++)
	if (cnt[i] > 0)
		glob_rev = mulmod(rev_fakt[cnt[i]],glob_rev);

for (var j=0; j<=half; j++) dp[j] = 0;
dp[0] = 1;
for (var i=0; i<52; i++)
	if (cnt[i] > 0)
		for (var j=half-cnt[i]; j>=0; j--)
			if (dp[j] > 0)
				dp[j + cnt[i]] = (dp[j + cnt[i]] + dp[j]) % 1000000007;

var solve_one = Array(52).fill(-1);

var solve_two = Array(52);
for (var j=0; j<52; j++)
	if (cnt[j] > 0) {
		var tt = Array(52).fill(-1);
		solve_two[j] = tt;
	}

var ee = [];

for (var i=0; i<qq; i++) {
	var a,b;
	var numbers = readline().split(" ").map(function(x) { return parseInt(x); });
	a = numbers[0]-1;
	b = numbers[1]-1;
	var a_ind = get_ind(s[a]);
	var b_ind = get_ind(s[b]);

	var total = cnt[a_ind] + cnt[b_ind];
	if (a_ind === b_ind)
		total -= cnt[b_ind];

	if (total > half) {
		ee.push(0);
		continue;
	}

	if (a_ind > b_ind) a_ind = b_ind + (b_ind=a_ind, 0);   // swap

	if (a_ind !== b_ind) {
		if (solve_two[a_ind][b_ind] === -1) {
			var tt = [];
			tt.push(a_ind);
			tt.push(b_ind);
			solve_two[a_ind][b_ind] = solve(tt);
		}
		ans = mulmod(mulmod(cnk(half, cnt[a_ind]), cnk(half - cnt[a_ind], cnt[b_ind]))*2, fakt[half]);
		ans = mulmod(mulmod(ans, fakt[half-cnt[a_ind]-cnt[b_ind]]), (glob_rev));
		ans = mulmod(mulmod(mulmod(ans,fakt[cnt[a_ind]]), fakt[cnt[b_ind]]), solve_two[a_ind][b_ind]);
	}
	else {
		if (solve_one[a_ind] === -1) {
			var tt = [];
			tt.push(a_ind);
			solve_one[a_ind] = solve(tt);
		}
		ans = mulmod(mulmod(mulmod(mulmod(mulmod(cnk(half, cnt[a_ind]), fakt[half])*2, fakt[half-cnt[a_ind]]), glob_rev), fakt[cnt[a_ind]]), solve_one[a_ind]);
	}
	ee.push(ans);
}

print(ee.join("\n"));

;(function (globalObject) {
  'use strict';

  var BigNumber,
    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
    mathceil = Math.ceil,
    mathfloor = Math.floor,
    bignumberError = '[BigNumber Error] ',
    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
    BASE = 1e14,
    LOG_BASE = 14,
    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
    SQRT_BASE = 1e7,
    MAX = 1E9;                                   // 0 to MAX_INT32

  function clone(configObject) {
    var div, convertBase, parseNumeric,
      P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
      ONE = new BigNumber(1),

      // The maximum number of decimal places for operations involving division.
      DECIMAL_PLACES = 1000,                   // 0 to MAX
      ROUNDING_MODE = 4,                       // 0 to 8 (look at ROUND_)

      // The exponent value at and beneath which toString returns exponential notation.
      TO_EXP_NEG = -1000,                      // 0 to -MAX
      // The exponent value at and above which toString returns exponential notation.
      TO_EXP_POS = 1000,                       // 0 to MAX
      MIN_EXP = -1e8,                          // -1 to -MAX
      MAX_EXP = 1e8,                           // 1 to MAX

      CRYPTO = false,                          // true or false
      MODULO_MODE = 1,                         // 0 to 9
      POW_PRECISION = 0,                       // 0 to MAX
      FORMAT = {
        prefix: '',
        groupSize: 3,
        secondaryGroupSize: 0,
        groupSeparator: ',',
        decimalSeparator: '.',
        fractionGroupSize: 0,
        fractionGroupSeparator: '\xA0',      // non-breaking space
        suffix: ''
      },
      ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';

    function BigNumber(n, b) {
      var alphabet, c, caseChanged, e, i, isNum, len, str,
        x = this;
      if (!(x instanceof BigNumber)) {
        return new BigNumber(n, b);
      }
      if (b == null) {
        if (n instanceof BigNumber) {
          x.s = n.s;
          x.e = n.e;
          x.c = (n = n.c) ? n.slice() : n;
          return;
        }
        isNum = typeof n == 'number';
        if (isNum && n * 0 == 0) {
          x.s = 1 / n < 0 ? (n = -n, -1) : 1;
          if (n === ~~n) {
            for (e = 0, i = n; i >= 10; i /= 10, e++);
            x.e = e;
            x.c = [n];
            return;
          }
          str = String(n);
        } else {
          str = String(n);
          if (!isNumeric.test(str)) return parseNumeric(x, str, isNum);
          x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
        }
        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
        if ((i = str.search(/e/i)) > 0) {
          if (e < 0) e = i;
          e += +str.slice(i + 1);
          str = str.substring(0, i);
        } else if (e < 0) {
          e = str.length;
        }
      } else {
        intCheck(b, 2, ALPHABET.length, 'Base');
        str = String(n);
        if (b == 10) {
          x = new BigNumber(n instanceof BigNumber ? n : str);
          return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
        }
        isNum = typeof n == 'number';
        if (isNum) {
          if (n * 0 != 0) return parseNumeric(x, str, isNum, b);
          x.s = 1 / n < 0 ? (str = str.slice(1), -1) : 1;
          if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
            throw Error
             (tooManyDigits + n);
          }
          isNum = false;
        } else {
          x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
        }
        alphabet = ALPHABET.slice(0, b);
        e = i = 0;
        for (len = str.length; i < len; i++) {
          if (alphabet.indexOf(c = str.charAt(i)) < 0) {
            if (c == '.') {
              if (i > e) {
                e = len;
                continue;
              }
            } else if (!caseChanged) {
              if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
                  str == str.toLowerCase() && (str = str.toUpperCase())) {
                caseChanged = true;
                i = -1;
                e = 0;
                continue;
              }
            }
            return parseNumeric(x, String(n), isNum, b);
          }
        }
        str = convertBase(str, b, 10, x.s);
        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
        else e = str.length;
      }
      for (i = 0; str.charCodeAt(i) === 48; i++);
      for (len = str.length; str.charCodeAt(--len) === 48;);
      str = str.slice(i, ++len);
      if (str) {
        len -= i;
        if (isNum && BigNumber.DEBUG &&
          len > 15 && (n > MAX_SAFE_INTEGER || n !== mathfloor(n))) {
            throw Error
             (tooManyDigits + (x.s * n));
        }
        e = e - i - 1;
        if (e > MAX_EXP) {
          x.c = x.e = null;
        } else if (e < MIN_EXP) {
          x.c = [x.e = 0];
        } else {
          x.e = e;
          x.c = [];
          i = (e + 1) % LOG_BASE;
          if (e < 0) i += LOG_BASE;
          if (i < len) {
            if (i) x.c.push(+str.slice(0, i));
            for (len -= LOG_BASE; i < len;) {
              x.c.push(+str.slice(i, i += LOG_BASE));
            }
            str = str.slice(i);
            i = LOG_BASE - str.length;
          } else {
            i -= len;
          }
          for (; i--; str += '0');
          x.c.push(+str);
        }
      } else {
        x.c = [x.e = 0];
      }
    }

    BigNumber.clone = clone;
    BigNumber.ROUND_UP = 0;
    BigNumber.ROUND_DOWN = 1;
    BigNumber.ROUND_CEIL = 2;
    BigNumber.ROUND_FLOOR = 3;
    BigNumber.ROUND_HALF_UP = 4;
    BigNumber.ROUND_HALF_DOWN = 5;
    BigNumber.ROUND_HALF_EVEN = 6;
    BigNumber.ROUND_HALF_CEIL = 7;
    BigNumber.ROUND_HALF_FLOOR = 8;
    BigNumber.EUCLID = 9;

    BigNumber.config = BigNumber.set = function (obj) {
      var p, v;
      if (obj != null) {
        if (typeof obj == 'object') {
          if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
            v = obj[p];
            intCheck(v, 0, MAX, p);
            DECIMAL_PLACES = v;
          }
          if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
            v = obj[p];
            intCheck(v, 0, 8, p);
            ROUNDING_MODE = v;
          }
          if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
            v = obj[p];
            if (v && v.pop) {
              intCheck(v[0], -MAX, 0, p);
              intCheck(v[1], 0, MAX, p);
              TO_EXP_NEG = v[0];
              TO_EXP_POS = v[1];
            } else {
              intCheck(v, -MAX, MAX, p);
              TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
            }
          }
          if (obj.hasOwnProperty(p = 'RANGE')) {
            v = obj[p];
            if (v && v.pop) {
              intCheck(v[0], -MAX, -1, p);
              intCheck(v[1], 1, MAX, p);
              MIN_EXP = v[0];
              MAX_EXP = v[1];
            } else {
              intCheck(v, -MAX, MAX, p);
              if (v) {
                MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
              } else {
                throw Error
                 (bignumberError + p + ' cannot be zero: ' + v);
              }
            }
          }
          if (obj.hasOwnProperty(p = 'CRYPTO')) {
            v = obj[p];
            if (v === !!v) {
              if (v) {
                if (typeof crypto != 'undefined' && crypto &&
                 (crypto.getRandomValues || crypto.randomBytes)) {
                  CRYPTO = v;
                } else {
                  CRYPTO = !v;
                  throw Error
                   (bignumberError + 'crypto unavailable');
                }
              } else {
                CRYPTO = v;
              }
            } else {
              throw Error
               (bignumberError + p + ' not true or false: ' + v);
            }
          }
          if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
            v = obj[p];
            intCheck(v, 0, 9, p);
            MODULO_MODE = v;
          }
          if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
            v = obj[p];
            intCheck(v, 0, MAX, p);
            POW_PRECISION = v;
          }
          if (obj.hasOwnProperty(p = 'FORMAT')) {
            v = obj[p];
            if (typeof v == 'object') FORMAT = v;
            else throw Error
             (bignumberError + p + ' not an object: ' + v);
          }
          if (obj.hasOwnProperty(p = 'ALPHABET')) {
            v = obj[p];
            if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
              ALPHABET = v;
            } else {
              throw Error
               (bignumberError + p + ' invalid: ' + v);
            }
          }
        } else {
          throw Error
           (bignumberError + 'Object expected: ' + obj);
        }
      }

      return {
        DECIMAL_PLACES: DECIMAL_PLACES,
        ROUNDING_MODE: ROUNDING_MODE,
        EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
        RANGE: [MIN_EXP, MAX_EXP],
        CRYPTO: CRYPTO,
        MODULO_MODE: MODULO_MODE,
        POW_PRECISION: POW_PRECISION,
        FORMAT: FORMAT,
        ALPHABET: ALPHABET
      };
    };

    BigNumber.isBigNumber = function (v) {
      return v instanceof BigNumber || v && v._isBigNumber === true || false;
    };

    BigNumber.maximum = BigNumber.max = function () {
      return maxOrMin(arguments, P.lt);
    };

    BigNumber.minimum = BigNumber.min = function () {
      return maxOrMin(arguments, P.gt);
    };

    BigNumber.random = (function () {
      var pow2_53 = 0x20000000000000;
      var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
       ? function () { return mathfloor(Math.random() * pow2_53); }
       : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
         (Math.random() * 0x800000 | 0); };
      return function (dp) {
        var a, b, e, k, v,
          i = 0,
          c = [],
          rand = new BigNumber(ONE);
        if (dp == null) dp = DECIMAL_PLACES;
        else intCheck(dp, 0, MAX);
        k = mathceil(dp / LOG_BASE);
        if (CRYPTO) {
          if (crypto.getRandomValues) {
            a = crypto.getRandomValues(new Uint32Array(k *= 2));
            for (; i < k;) {
              v = a[i] * 0x20000 + (a[i + 1] >>> 11);
              if (v >= 9e15) {
                b = crypto.getRandomValues(new Uint32Array(2));
                a[i] = b[0];
                a[i + 1] = b[1];
              } else {
                c.push(v % 1e14);
                i += 2;
              }
            }
            i = k / 2;
          } else if (crypto.randomBytes) {
            a = crypto.randomBytes(k *= 7);
            for (; i < k;) {
              v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
                 (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
                 (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
              if (v >= 9e15) {
                crypto.randomBytes(7).copy(a, i);
              } else {
                c.push(v % 1e14);
                i += 7;
              }
            }
            i = k / 7;
          } else {
            CRYPTO = false;
            throw Error
             (bignumberError + 'crypto unavailable');
          }
        }
        if (!CRYPTO) {
          for (; i < k;) {
            v = random53bitInt();
            if (v < 9e15) c[i++] = v % 1e14;
          }
        }
        k = c[--i];
        dp %= LOG_BASE;
        if (k && dp) {
          v = POWS_TEN[LOG_BASE - dp];
          c[i] = mathfloor(k / v) * v;
        }
        for (; c[i] === 0; c.pop(), i--);
        if (i < 0) {
          c = [e = 0];
        } else {
          for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
          for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
          if (i < LOG_BASE) e -= LOG_BASE - i;
        }
        rand.e = e;
        rand.c = c;
        return rand;
      };
    })();

    BigNumber.sum = function () {
      var i = 1,
        args = arguments,
        sum = new BigNumber(args[0]);
      for (; i < args.length;) sum = sum.plus(args[i++]);
      return sum;
    };

    convertBase = (function () {
      var decimal = '0123456789';
      function toBaseOut(str, baseIn, baseOut, alphabet) {
        var j,
          arr = [0],
          arrL,
          i = 0,
          len = str.length;
        for (; i < len;) {
          for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
          arr[0] += alphabet.indexOf(str.charAt(i++));
          for (j = 0; j < arr.length; j++) {
            if (arr[j] > baseOut - 1) {
              if (arr[j + 1] == null) arr[j + 1] = 0;
              arr[j + 1] += arr[j] / baseOut | 0;
              arr[j] %= baseOut;
            }
          }
        }
        return arr.reverse();
      }
      return function (str, baseIn, baseOut, sign, callerIsToString) {
        var alphabet, d, e, k, r, x, xc, y,
          i = str.indexOf('.'),
          dp = DECIMAL_PLACES,
          rm = ROUNDING_MODE;
        if (i >= 0) {
          k = POW_PRECISION;
          POW_PRECISION = 0;
          str = str.replace('.', '');
          y = new BigNumber(baseIn);
          x = y.pow(str.length - i);
          POW_PRECISION = k;
          y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
           10, baseOut, decimal);
          y.e = y.c.length;
        }
        xc = toBaseOut(str, baseIn, baseOut, callerIsToString
         ? (alphabet = ALPHABET, decimal)
         : (alphabet = decimal, ALPHABET));
        e = k = xc.length;
        for (; xc[--k] == 0; xc.pop());
        if (!xc[0]) return alphabet.charAt(0);
        if (i < 0) {
          --e;
        } else {
          x.c = xc;
          x.e = e;
          x.s = sign;
          x = div(x, y, dp, rm, baseOut);
          xc = x.c;
          r = x.r;
          e = x.e;
        }
        d = e + dp + 1;
        i = xc[d];
        k = baseOut / 2;
        r = r || d < 0 || xc[d + 1] != null;
        r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
              : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
               rm == (x.s < 0 ? 8 : 7));
        if (d < 1 || !xc[0]) {
          str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
        } else {
          xc.length = d;
          if (r) {
            for (--baseOut; ++xc[--d] > baseOut;) {
              xc[d] = 0;
              if (!d) {
                ++e;
                xc = [1].concat(xc);
              }
            }
          }
          for (k = xc.length; !xc[--k];);
          for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
          str = toFixedPoint(str, e, alphabet.charAt(0));
        }
        return str;
      };
    })();

    div = (function () {
      function multiply(x, k, base) {
        var m, temp, xlo, xhi,
          carry = 0,
          i = x.length,
          klo = k % SQRT_BASE,
          khi = k / SQRT_BASE | 0;
        for (x = x.slice(); i--;) {
          xlo = x[i] % SQRT_BASE;
          xhi = x[i] / SQRT_BASE | 0;
          m = khi * xlo + xhi * klo;
          temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
          carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
          x[i] = temp % base;
        }
        if (carry) x = [carry].concat(x);
        return x;
      }

      function compare(a, b, aL, bL) {
        var i, cmp;
        if (aL != bL) {
          cmp = aL > bL ? 1 : -1;
        } else {
          for (i = cmp = 0; i < aL; i++) {
            if (a[i] != b[i]) {
              cmp = a[i] > b[i] ? 1 : -1;
              break;
            }
          }
        }
        return cmp;
      }

      function subtract(a, b, aL, base) {
        var i = 0;
        for (; aL--;) {
          a[aL] -= i;
          i = a[aL] < b[aL] ? 1 : 0;
          a[aL] = i * base + a[aL] - b[aL];
        }
        for (; !a[0] && a.length > 1; a.splice(0, 1));
      }
      return function (x, y, dp, rm, base) {
        var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
          yL, yz,
          s = x.s == y.s ? 1 : -1,
          xc = x.c,
          yc = y.c;
        if (!xc || !xc[0] || !yc || !yc[0]) {
          return new BigNumber(
           !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
            xc && xc[0] == 0 || !yc ? s * 0 : s / 0
         );
        }
        q = new BigNumber(s);
        qc = q.c = [];
        e = x.e - y.e;
        s = dp + e + 1;
        if (!base) {
          base = BASE;
          e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
          s = s / LOG_BASE | 0;
        }
        for (i = 0; yc[i] == (xc[i] || 0); i++);
        if (yc[i] > (xc[i] || 0)) e--;
        if (s < 0) {
          qc.push(1);
          more = true;
        } else {
          xL = xc.length;
          yL = yc.length;
          i = 0;
          s += 2;
          n = mathfloor(base / (yc[0] + 1));
          if (n > 1) {
            yc = multiply(yc, n, base);
            xc = multiply(xc, n, base);
            yL = yc.length;
            xL = xc.length;
          }
          xi = yL;
          rem = xc.slice(0, yL);
          remL = rem.length;
          for (; remL < yL; rem[remL++] = 0);
          yz = yc.slice();
          yz = [0].concat(yz);
          yc0 = yc[0];
          if (yc[1] >= base / 2) yc0++;
          do {
            n = 0;
            cmp = compare(yc, rem, yL, remL);
            if (cmp < 0) {
              rem0 = rem[0];
              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
              n = mathfloor(rem0 / yc0);
              if (n > 1) {
                if (n >= base) n = base - 1;
                prod = multiply(yc, n, base);
                prodL = prod.length;
                remL = rem.length;
                while (compare(prod, rem, prodL, remL) == 1) {
                  n--;
                  subtract(prod, yL < prodL ? yz : yc, prodL, base);
                  prodL = prod.length;
                  cmp = 1;
                }
              } else {
                if (n == 0) {
                  cmp = n = 1;
                }
                prod = yc.slice();
                prodL = prod.length;
              }
              if (prodL < remL) prod = [0].concat(prod);
              subtract(rem, prod, remL, base);
              remL = rem.length;
              if (cmp == -1) {
                while (compare(yc, rem, yL, remL) < 1) {
                  n++;
                  subtract(rem, yL < remL ? yz : yc, remL, base);
                  remL = rem.length;
                }
              }
            } else if (cmp === 0) {
              n++;
              rem = [0];
            }
            qc[i++] = n;
            if (rem[0]) {
              rem[remL++] = xc[xi] || 0;
            } else {
              rem = [xc[xi]];
              remL = 1;
            }
          } while ((xi++ < xL || rem[0] != null) && s--);
          more = rem[0] != null;
          if (!qc[0]) qc.splice(0, 1);
        }
        if (base == BASE) {
          for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
          round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
        } else {
          q.e = e;
          q.r = +more;
        }
        return q;
      };
    })();

    function format(n, i, rm, id) {
      var c0, e, ne, len, str;
      if (rm == null) rm = ROUNDING_MODE;
      else intCheck(rm, 0, 8);
      if (!n.c) return n.toString();
      c0 = n.c[0];
      ne = n.e;
      if (i == null) {
        str = coeffToString(n.c);
        str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
         ? toExponential(str, ne)
         : toFixedPoint(str, ne, '0');
      } else {
        n = round(new BigNumber(n), i, rm);
        e = n.e;
        str = coeffToString(n.c);
        len = str.length;
        if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
          for (; len < i; str += '0', len++);
          str = toExponential(str, e);
        } else {
          i -= ne;
          str = toFixedPoint(str, e, '0');
          if (e + 1 > len) {
            if (--i > 0) for (str += '.'; i--; str += '0');
          } else {
            i += e - len;
            if (i > 0) {
              if (e + 1 == len) str += '.';
              for (; i--; str += '0');
            }
          }
        }
      }
      return n.s < 0 && c0 ? '-' + str : str;
    }

    function maxOrMin(args, method) {
      var n,
        i = 1,
        m = new BigNumber(args[0]);
      for (; i < args.length; i++) {
        n = new BigNumber(args[i]);
        if (!n.s) {
          m = n;
          break;
        } else if (method.call(m, n)) {
          m = n;
        }
      }
      return m;
    }

    function normalise(n, c, e) {
      var i = 1,
        j = c.length;
      for (; !c[--j]; c.pop());
      for (j = c[0]; j >= 10; j /= 10, i++);
      if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
        n.c = n.e = null;
      } else if (e < MIN_EXP) {
        n.c = [n.e = 0];
      } else {
        n.e = e;
        n.c = c;
      }
      return n;
    }

    parseNumeric = (function () {
      var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
        dotAfter = /^([^.]+)\.$/,
        dotBefore = /^\.([^.]+)$/,
        isInfinityOrNaN = /^-?(Infinity|NaN)$/,
        whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
      return function (x, str, isNum, b) {
        var base,
          s = isNum ? str : str.replace(whitespaceOrPlus, '');
        if (isInfinityOrNaN.test(s)) {
          x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
          x.c = x.e = null;
        } else {
          if (!isNum) {
            s = s.replace(basePrefix, function (m, p1, p2) {
              base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
              return !b || b == base ? p1 : m;
            });
            if (b) {
              base = b;
              s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
            }
            if (str != s) return new BigNumber(s, base);
          }
          if (BigNumber.DEBUG) {
            throw Error
              (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
          }
          x.c = x.e = x.s = null;
        }
      }
    })();

    function round(x, sd, rm, r) {
      var d, i, j, k, n, ni, rd,
        xc = x.c,
        pows10 = POWS_TEN;
      if (xc) {
        out: {
          for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
          i = sd - d;
          if (i < 0) {
            i += LOG_BASE;
            j = sd;
            n = xc[ni = 0];
            rd = n / pows10[d - j - 1] % 10 | 0;
          } else {
            ni = mathceil((i + 1) / LOG_BASE);
            if (ni >= xc.length) {
              if (r) {
                for (; xc.length <= ni; xc.push(0));
                n = rd = 0;
                d = 1;
                i %= LOG_BASE;
                j = i - LOG_BASE + 1;
              } else {
                break out;
              }
            } else {
              n = k = xc[ni];
              for (d = 1; k >= 10; k /= 10, d++);
              i %= LOG_BASE;
              j = i - LOG_BASE + d;
              rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
            }
          }
          r = r || sd < 0 ||
           xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
          r = rm < 4
           ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
           : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
            ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
             rm == (x.s < 0 ? 8 : 7));
          if (sd < 1 || !xc[0]) {
            xc.length = 0;
            if (r) {
              sd -= x.e + 1;
              xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
              x.e = -sd || 0;
            } else {
              xc[0] = x.e = 0;
            }
            return x;
          }
          if (i == 0) {
            xc.length = ni;
            k = 1;
            ni--;
          } else {
            xc.length = ni + 1;
            k = pows10[LOG_BASE - i];
            xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
          }
          if (r) {
            for (; ;) {
              if (ni == 0) {
                for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
                j = xc[0] += k;
                for (k = 1; j >= 10; j /= 10, k++);
                if (i != k) {
                  x.e++;
                  if (xc[0] == BASE) xc[0] = 1;
                }
                break;
              } else {
                xc[ni] += k;
                if (xc[ni] != BASE) break;
                xc[ni--] = 0;
                k = 1;
              }
            }
          }
          for (i = xc.length; xc[--i] === 0; xc.pop());
        }
        if (x.e > MAX_EXP) {
          x.c = x.e = null;
        } else if (x.e < MIN_EXP) {
          x.c = [x.e = 0];
        }
      }
      return x;
    }

    function valueOf(n) {
      var str,
        e = n.e;
      if (e === null) return n.toString();
      str = coeffToString(n.c);
      str = e <= TO_EXP_NEG || e >= TO_EXP_POS
        ? toExponential(str, e)
        : toFixedPoint(str, e, '0');
      return n.s < 0 ? '-' + str : str;
    }

    P.absoluteValue = P.abs = function () {
      var x = new BigNumber(this);
      if (x.s < 0) x.s = 1;
      return x;
    };

    P.comparedTo = function (y, b) {
      return compare(this, new BigNumber(y, b));
    };

    P.decimalPlaces = P.dp = function (dp, rm) {
      var c, n, v,
        x = this;
      if (dp != null) {
        intCheck(dp, 0, MAX);
        if (rm == null) rm = ROUNDING_MODE;
        else intCheck(rm, 0, 8);
        return round(new BigNumber(x), dp + x.e + 1, rm);
      }
      if (!(c = x.c)) return null;
      n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
      if (v = c[v]) for (; v % 10 == 0; v /= 10, n--);
      if (n < 0) n = 0;
      return n;
    };

    P.dividedBy = P.div = function (y, b) {
      return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
    };

    P.dividedToIntegerBy = P.idiv = function (y, b) {
      return div(this, new BigNumber(y, b), 0, 1);
    };

    P.exponentiatedBy = P.pow = function (n, m) {
      var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
        x = this;
      n = new BigNumber(n);
      if (n.c && !n.isInteger()) {
        throw Error
          (bignumberError + 'Exponent not an integer: ' + valueOf(n));
      }
      if (m != null) m = new BigNumber(m);
      nIsBig = n.e > 14;
      if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
        y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
        return m ? y.mod(m) : y;
      }
      nIsNeg = n.s < 0;
      if (m) {
        if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
        isModExp = !nIsNeg && x.isInteger() && m.isInteger();
        if (isModExp) x = x.mod(m);
      } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
        ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
        : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
        k = x.s < 0 && isOdd(n) ? -0 : 0;
        if (x.e > -1) k = 1 / k;
        return new BigNumber(nIsNeg ? 1 / k : k);
      } else if (POW_PRECISION) {
        k = mathceil(POW_PRECISION / LOG_BASE + 2);
      }
      if (nIsBig) {
        half = new BigNumber(0.5);
        if (nIsNeg) n.s = 1;
        nIsOdd = isOdd(n);
      } else {
        i = Math.abs(+valueOf(n));
        nIsOdd = i % 2;
      }
      y = new BigNumber(ONE);
      for (; ;) {
        if (nIsOdd) {
          y = y.times(x);
          if (!y.c) break;

          if (k) {
            if (y.c.length > k) y.c.length = k;
          } else if (isModExp) {
            y = y.mod(m);
          }
        }
        if (i) {
          i = mathfloor(i / 2);
          if (i === 0) break;
          nIsOdd = i % 2;
        } else {
          n = n.times(half);
          round(n, n.e + 1, 1);
          if (n.e > 14) {
            nIsOdd = isOdd(n);
          } else {
            i = +valueOf(n);
            if (i === 0) break;
            nIsOdd = i % 2;
          }
        }
        x = x.times(x);
        if (k) {
          if (x.c && x.c.length > k) x.c.length = k;
        } else if (isModExp) {
          x = x.mod(m);
        }
      }
      if (isModExp) return y;
      if (nIsNeg) y = ONE.div(y);
      return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
    };

    P.integerValue = function (rm) {
      var n = new BigNumber(this);
      if (rm == null) rm = ROUNDING_MODE;
      else intCheck(rm, 0, 8);
      return round(n, n.e + 1, rm);
    };

    P.isEqualTo = P.eq = function (y, b) {
      return compare(this, new BigNumber(y, b)) === 0;
    };

    P.isFinite = function () {
      return !!this.c;
    };

    P.isGreaterThan = P.gt = function (y, b) {
      return compare(this, new BigNumber(y, b)) > 0;
    };

    P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
      return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;

    };

    P.isInteger = function () {
      return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
    };

    P.isLessThan = P.lt = function (y, b) {
      return compare(this, new BigNumber(y, b)) < 0;
    };

    P.isLessThanOrEqualTo = P.lte = function (y, b) {
      return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
    };

    P.isNaN = function () {
      return !this.s;
    };

    P.isNegative = function () {
      return this.s < 0;
    };

    P.isPositive = function () {
      return this.s > 0;
    };

    P.isZero = function () {
      return !!this.c && this.c[0] == 0;
    };

    P.minus = function (y, b) {
      var i, j, t, xLTy,
        x = this,
        a = x.s;
      y = new BigNumber(y, b);
      b = y.s;
      if (!a || !b) return new BigNumber(NaN);
      if (a != b) {
        y.s = -b;
        return x.plus(y);
      }
      var xe = x.e / LOG_BASE,
        ye = y.e / LOG_BASE,
        xc = x.c,
        yc = y.c;
      if (!xe || !ye) {
        if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
        if (!xc[0] || !yc[0]) {
          return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
           ROUNDING_MODE == 3 ? -0 : 0);
        }
      }
      xe = bitFloor(xe);
      ye = bitFloor(ye);
      xc = xc.slice();
      if (a = xe - ye) {
        if (xLTy = a < 0) {
          a = -a;
          t = xc;
        } else {
          ye = xe;
          t = yc;
        }
        t.reverse();
        for (b = a; b--; t.push(0));
        t.reverse();
      } else {
        j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
        for (a = b = 0; b < j; b++) {
          if (xc[b] != yc[b]) {
            xLTy = xc[b] < yc[b];
            break;
          }
        }
      }
      if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
      b = (j = yc.length) - (i = xc.length);
      if (b > 0) for (; b--; xc[i++] = 0);
      b = BASE - 1;
      for (; j > a;) {
        if (xc[--j] < yc[j]) {
          for (i = j; i && !xc[--i]; xc[i] = b);
          --xc[i];
          xc[j] += BASE;
        }

        xc[j] -= yc[j];
      }
      for (; xc[0] == 0; xc.splice(0, 1), --ye);
      if (!xc[0]) {
        y.s = ROUNDING_MODE == 3 ? -1 : 1;
        y.c = [y.e = 0];
        return y;
      }
      return normalise(y, xc, ye);
    };

    P.modulo = P.mod = function (y, b) {
      var q, s,
        x = this;
      y = new BigNumber(y, b);
      if (!x.c || !y.s || y.c && !y.c[0]) {
        return new BigNumber(NaN);
      } else if (!y.c || x.c && !x.c[0]) {
        return new BigNumber(x);
      }
      if (MODULO_MODE == 9) {
        s = y.s;
        y.s = 1;
        q = div(x, y, 0, 3);
        y.s = s;
        q.s *= s;
      } else {
        q = div(x, y, 0, MODULO_MODE);
      }
      y = x.minus(q.times(y));
      if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
      return y;
    };

    P.multipliedBy = P.times = function (y, b) {
      var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
        base, sqrtBase,
        x = this,
        xc = x.c,
        yc = (y = new BigNumber(y, b)).c;
      if (!xc || !yc || !xc[0] || !yc[0]) {
        if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
          y.c = y.e = y.s = null;
        } else {
          y.s *= x.s;
          if (!xc || !yc) {
            y.c = y.e = null;
          } else {
            y.c = [0];
            y.e = 0;
          }
        }
        return y;
      }
      e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
      y.s *= x.s;
      xcL = xc.length;
      ycL = yc.length;
      if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
      for (i = xcL + ycL, zc = []; i--; zc.push(0));
      base = BASE;
      sqrtBase = SQRT_BASE;
      for (i = ycL; --i >= 0;) {
        c = 0;
        ylo = yc[i] % sqrtBase;
        yhi = yc[i] / sqrtBase | 0;
        for (k = xcL, j = i + k; j > i;) {
          xlo = xc[--k] % sqrtBase;
          xhi = xc[k] / sqrtBase | 0;
          m = yhi * xlo + xhi * ylo;
          xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
          c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
          zc[j--] = xlo % base;
        }
        zc[j] = c;
      }
      if (c) {
        ++e;
      } else {
        zc.splice(0, 1);
      }
      return normalise(y, zc, e);
    };

    P.negated = function () {
      var x = new BigNumber(this);
      x.s = -x.s || null;
      return x;
    };

    P.plus = function (y, b) {
      var t,
        x = this,
        a = x.s;
      y = new BigNumber(y, b);
      b = y.s;
      if (!a || !b) return new BigNumber(NaN);
       if (a != b) {
        y.s = -b;
        return x.minus(y);
      }
      var xe = x.e / LOG_BASE,
        ye = y.e / LOG_BASE,
        xc = x.c,
        yc = y.c;
      if (!xe || !ye) {
        if (!xc || !yc) return new BigNumber(a / 0);
        if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
      }
      xe = bitFloor(xe);
      ye = bitFloor(ye);
      xc = xc.slice();
      if (a = xe - ye) {
        if (a > 0) {
          ye = xe;
          t = yc;
        } else {
          a = -a;
          t = xc;
        }
        t.reverse();
        for (; a--; t.push(0));
        t.reverse();
      }
      a = xc.length;
      b = yc.length;
      if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
      for (a = 0; b;) {
        a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
        xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
      }
      if (a) {
        xc = [a].concat(xc);
        ++ye;
      }
      return normalise(y, xc, ye);
    };

    P.precision = P.sd = function (sd, rm) {
      var c, n, v,
        x = this;
      if (sd != null && sd !== !!sd) {
        intCheck(sd, 1, MAX);
        if (rm == null) rm = ROUNDING_MODE;
        else intCheck(rm, 0, 8);
        return round(new BigNumber(x), sd, rm);
      }
      if (!(c = x.c)) return null;
      v = c.length - 1;
      n = v * LOG_BASE + 1;
      if (v = c[v]) {
        for (; v % 10 == 0; v /= 10, n--);
        for (v = c[0]; v >= 10; v /= 10, n++);
      }
      if (sd && x.e + 1 > n) n = x.e + 1;
      return n;
    };
    P.shiftedBy = function (k) {
      intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
      return this.times('1e' + k);
    };
    P.squareRoot = P.sqrt = function () {
      var m, n, r, rep, t,
        x = this,
        c = x.c,
        s = x.s,
        e = x.e,
        dp = DECIMAL_PLACES + 4,
        half = new BigNumber('0.5');
      if (s !== 1 || !c || !c[0]) {
        return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
      }
      s = Math.sqrt(+valueOf(x));
      if (s == 0 || s == 1 / 0) {
        n = coeffToString(c);
        if ((n.length + e) % 2 == 0) n += '0';
        s = Math.sqrt(+n);
        e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);

        if (s == 1 / 0) {
          n = '1e' + e;
        } else {
          n = s.toExponential();
          n = n.slice(0, n.indexOf('e') + 1) + e;
        }
        r = new BigNumber(n);
      } else {
        r = new BigNumber(s + '');
      }
      if (r.c[0]) {
        e = r.e;
        s = e + dp;
        if (s < 3) s = 0;
        for (; ;) {
          t = r;
          r = half.times(t.plus(div(x, t, dp, 1)));
          if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
            if (r.e < e) --s;
            n = n.slice(s - 3, s + 1);
            if (n == '9999' || !rep && n == '4999') {
              if (!rep) {
                round(t, t.e + DECIMAL_PLACES + 2, 0);

                if (t.times(t).eq(x)) {
                  r = t;
                  break;
                }
              }
              dp += 4;
              s += 4;
              rep = 1;
            } else {
              if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
                round(r, r.e + DECIMAL_PLACES + 2, 1);
                m = !r.times(r).eq(x);
              }
              break;
            }
          }
        }
      }

      return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
    };

    P.toExponential = function (dp, rm) {
      if (dp != null) {
        intCheck(dp, 0, MAX);
        dp++;
      }
      return format(this, dp, rm, 1);
    };

    P.toFixed = function (dp, rm) {
      if (dp != null) {
        intCheck(dp, 0, MAX);
        dp = dp + this.e + 1;
      }
      return format(this, dp, rm);
    };

    P.toFormat = function (dp, rm, format) {
      var str,
        x = this;

      if (format == null) {
        if (dp != null && rm && typeof rm == 'object') {
          format = rm;
          rm = null;
        } else if (dp && typeof dp == 'object') {
          format = dp;
          dp = rm = null;
        } else {
          format = FORMAT;
        }
      } else if (typeof format != 'object') {
        throw Error
          (bignumberError + 'Argument not an object: ' + format);
      }

      str = x.toFixed(dp, rm);

      if (x.c) {
        var i,
          arr = str.split('.'),
          g1 = +format.groupSize,
          g2 = +format.secondaryGroupSize,
          groupSeparator = format.groupSeparator || '',
          intPart = arr[0],
          fractionPart = arr[1],
          isNeg = x.s < 0,
          intDigits = isNeg ? intPart.slice(1) : intPart,
          len = intDigits.length;

        if (g2) i = g1, g1 = g2, g2 = i, len -= i;

        if (g1 > 0 && len > 0) {
          i = len % g1 || g1;
          intPart = intDigits.substr(0, i);
          for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
          if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
          if (isNeg) intPart = '-' + intPart;
        }

        str = fractionPart
         ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
          ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
           '$&' + (format.fractionGroupSeparator || ''))
          : fractionPart)
         : intPart;
      }

      return (format.prefix || '') + str + (format.suffix || '');
    };

    P.toFraction = function (md) {
      var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
        x = this,
        xc = x.c;

      if (md != null) {
        n = new BigNumber(md);
        if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
          throw Error
            (bignumberError + 'Argument ' +
              (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
        }
      }

      if (!xc) return new BigNumber(x);

      d = new BigNumber(ONE);
      n1 = d0 = new BigNumber(ONE);
      d1 = n0 = new BigNumber(ONE);
      s = coeffToString(xc);

      e = d.e = s.length - x.e - 1;
      d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
      md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;

      exp = MAX_EXP;
      MAX_EXP = 1 / 0;
      n = new BigNumber(s);
      n0.c[0] = 0;

      for (; ;)  {
        q = div(n, d, 0, 1);
        d2 = d0.plus(q.times(d1));
        if (d2.comparedTo(md) == 1) break;
        d0 = d1;
        d1 = d2;
        n1 = n0.plus(q.times(d2 = n1));
        n0 = d2;
        d = n.minus(q.times(d2 = d));
        n = d2;
      }

      d2 = div(md.minus(d0), d1, 0, 1);
      n0 = n0.plus(d2.times(n1));
      d0 = d0.plus(d2.times(d1));
      n0.s = n1.s = x.s;
      e = e * 2;

      r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
          div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
      MAX_EXP = exp;

      return r;
    };

    P.toNumber = function () {
      return +valueOf(this);
    };

    P.toPrecision = function (sd, rm) {
      if (sd != null) intCheck(sd, 1, MAX);
      return format(this, sd, rm, 2);
    };

    P.toString = function (b) {
      var str,
        n = this,
        s = n.s,
        e = n.e;

      if (e === null) {
        if (s) {
          str = 'Infinity';
          if (s < 0) str = '-' + str;
        } else {
          str = 'NaN';
        }
      } else {
        if (b == null) {
          str = e <= TO_EXP_NEG || e >= TO_EXP_POS
           ? toExponential(coeffToString(n.c), e)
           : toFixedPoint(coeffToString(n.c), e, '0');
        } else if (b === 10) {
          n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
          str = toFixedPoint(coeffToString(n.c), n.e, '0');
        } else {
          intCheck(b, 2, ALPHABET.length, 'Base');
          str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
        }

        if (s < 0 && n.c[0]) str = '-' + str;
      }

      return str;
    };

    P.valueOf = P.toJSON = function () {
      return valueOf(this);
    };

    P._isBigNumber = true;
    if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
      P[Symbol.toStringTag] = 'BigNumber';
      P[Symbol.for('nodejs.util.inspect.custom')] = P.valueOf;
    }
    if (configObject != null) BigNumber.set(configObject);
    return BigNumber;
  }

  function bitFloor(n) {
    var i = n | 0;
    return n > 0 || n === i ? i : i - 1;
  }

  function coeffToString(a) {
    var s, z,
      i = 1,
      j = a.length,
      r = a[0] + '';
    for (; i < j;) {
      s = a[i++] + '';
      z = LOG_BASE - s.length;
      for (; z--; s = '0' + s);
      r += s;
    }
    for (j = r.length; r.charCodeAt(--j) === 48;);
    return r.slice(0, j + 1 || 1);
  }

  function compare(x, y) {
    var a, b,
      xc = x.c,
      yc = y.c,
      i = x.s,
      j = y.s,
      k = x.e,
      l = y.e;
    if (!i || !j) return null;
    a = xc && !xc[0];
    b = yc && !yc[0];
    if (a || b) return a ? b ? 0 : -j : i;
    if (i != j) return i;
    a = i < 0;
    b = k == l;
    if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
    if (!b) return k > l ^ a ? 1 : -1;
    j = (k = xc.length) < (l = yc.length) ? k : l;
    for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
    return k == l ? 0 : k > l ^ a ? 1 : -1;
  }

  function intCheck(n, min, max, name) {
    if (n < min || n > max || n !== (n < 0 ? mathceil(n) : mathfloor(n))) {
      throw Error
       (bignumberError + (name || 'Argument') + (typeof n == 'number'
         ? n < min || n > max ? ' out of range: ' : ' not an integer: '
         : ' not a primitive number: ') + String(n));
    }
  }

  function isOdd(n) {
    var k = n.c.length - 1;
    return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
  }

  function toExponential(str, e) {
    return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
     (e < 0 ? 'e' : 'e+') + e;
  }

  function toFixedPoint(str, e, z) {
    var len, zs;
    if (e < 0) {
      for (zs = z + '.'; ++e; zs += z);
      str = zs + str;
    } else {
      len = str.length;
      if (++e > len) {
        for (zs = z, e -= len; --e; zs += z);
        str += zs;
      } else if (e < len) {
        str = str.slice(0, e) + '.' + str.slice(e);
      }
    }
    return str;
  }

  BigNumber = clone();
  BigNumber['default'] = BigNumber.BigNumber = BigNumber;
  if (typeof define == 'function' && define.amd) {
    define(function () { return BigNumber; });
  } else if (typeof module != 'undefined' && module.exports) {
    module.exports = BigNumber;
  } else {
    if (!globalObject) {
      globalObject = typeof self != 'undefined' && self ? self : window;
    }
    globalObject.BigNumber = BigNumber;
  }
})(this);

//var qq = readline().split(" ").map(function(x) { return parseInt(x); });
var s = readline();
var qq = readline().split(" ").map(function(x) { return parseInt(x); })[0];

var cnt = Array(52).fill(0);
const ALPHABET = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';

get_ind = function (c) {
 	return ALPHABET.indexOf(c);
};

var MODULE = new BigNumber(1000000007);

find_deg = function(x, deg, MODULE) {
	var b = 1, a = x;
	while (deg > 0) {
		if (deg % 2 === 1)
			b = Number(BigNumber(b).times(a).mod(MODULE));
		deg = Math.floor(deg / 2);
		if (deg > 0)
			a = Number(BigNumber(a).times(a).mod(MODULE));
	}
	return Number(b);
};

find_rev = function(x, MODULE) {
	return find_deg(x, MODULE-2, MODULE);
};

var fakt = Array(s.length+1).fill(0);
var rev_fakt = Array(s.length+1).fill(0);

cnk = function(n, k) {
	return Number(BigNumber(fakt[n]).times(rev_fakt[k]).times(rev_fakt[n-k]).mod(MODULE));
}

for (var i=0; i<s.length; i++)
	cnt[get_ind(s[i])]++;

var half = Math.floor(s.length / 2);

var ans = new BigNumber(0);
var total_ans = 0;

fakt[0] = 1; fakt[1] = 1;
for (var i=2; i<=s.length; i++)
	fakt[i] = Number(BigNumber(fakt[i-1]).times(i).mod(MODULE));

rev_fakt[0] = 1; rev_fakt[1] = 1;
rev_fakt[s.length] = find_rev(fakt[s.length], MODULE);
for (var i = s.length - 1; i > 1; i--)
	rev_fakt[i] = Number(BigNumber(rev_fakt[i+1]).times(i+1).mod(MODULE));

var glob_rev = 1;
for (var i=0; i<52; i++)
	if (cnt[i] > 0)
		glob_rev = Number(BigNumber(rev_fakt[cnt[i]]).times(glob_rev).mod(MODULE));

for (var i=0; i<qq; i++) {
	var a,b;
	var numbers = readline().split(" ").map(function(x) { return parseInt(x); });
	a = numbers[0]-1;
	b = numbers[1]-1;
	var a_ind = get_ind(s[a]);
	var b_ind = get_ind(s[b]);

	var total = cnt[a_ind] + cnt[b_ind];
	if (a_ind === b_ind)
		total -= cnt[b_ind];

	if (total > half) {
		print("0");
		continue;
	}

	if (a_ind !== b_ind)
		ans = BigNumber(cnk(half, cnt[a_ind])).times(cnk(half - cnt[a_ind], cnt[b_ind])).times(2).times(glob_rev).times(fakt[cnt[a_ind]]).times(fakt[cnt[b_ind]]).times(fakt[half*2-cnt[a_ind]-cnt[b_ind]]).mod(MODULE);
	else
		ans = BigNumber(cnk(half, cnt[a_ind])).times(2).times(glob_rev).times(fakt[cnt[a_ind]]).times(fakt[half*2-cnt[a_ind]]).mod(MODULE);
	print(Number(ans));
}

var s = readline();
var qq = readline().split(" ").map(function(x) { return parseInt(x); })[0];

var cnt = Array(52).fill(0);

const ALPHABET = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';
get_ind = function (c) {
 	return ALPHABET.indexOf(c);
};

const MOD = 1000000007;

mulmod = function(a, b) {
  if (a < b) a = b + (b=a, 0);   // swap
  var x = 0, y = a % MOD;
  while (b) {
    if (b & 1) {
    	x += y;
    	if (x >= MOD) x -= MOD;
    }
    y <<= 1;
    if (y >= MOD) y -= MOD;
    b >>= 1;
  }
  return x;
}

find_deg = function(x, deg) {
	var b = 1, a = x % MOD;
	while (deg) {
		if (deg & 1) b = mulmod(b, a);
		deg >>= 1;
		if (deg > 0) a = mulmod(a, a);
	}
	return b % MOD;
};

find_rev = function(x) {
	return find_deg(x, MOD-2);   // MOD is prime, so MOD-2 is correct Phi-1 value
};

var fakt = Array(s.length+1).fill(0);
var rev_fakt = Array(s.length+1).fill(0);

cnk = function(n, k) {
	return mulmod(mulmod(fakt[n], rev_fakt[k]), rev_fakt[n-k]);
}

var half = Math.floor(s.length / 2);
var dp = Array(half + 1).fill(0);

solve = function(wei) {
	var sum_way = 0;
	for (var i=0; i<wei.length; i++) sum_way += wei[i];
	if (sum_way < half)
		return 0;

	var WW = [];
	var total_W = half;
	for (var i=0; i<wei.length; i++)
		if (wei[i] <= total_W && sum_way - wei[i] < total_W) {
			total_W -= wei[i];
			sum_way -= wei[i];
		}
		else
			if (wei[i] <= total_W)
				WW.push(wei[i]);

	for (var j=0; j<=total_W; j++)
		dp[j] = 0;
	dp[0] = 1;
	var all_wei = [];
	all_wei.push(0);
	for (var i=0; i<WW.length; i++) {
		var len = all_wei.length;
		for (var j=len-1; j>=0; j--)
			if (all_wei[j] + WW[i] <= total_W) {
				if (dp[all_wei[j] + WW[i]] <= 0)
					all_wei.push(all_wei[j] + WW[i]);
				dp[all_wei[j] + WW[i]] = (dp[all_wei[j] + WW[i]] + dp[all_wei[j]]) % 1000000007;
			}
		if (i+1 < WW.length)
			all_wei.sort(function(a,b) {return a-b;});
	}
	return dp[total_W];
}

for (var i=0; i<s.length; i++)
	cnt[get_ind(s[i])]++;

var ans = 0;

var inv = Array(s.length+1).fill(0);
inv[1] = 1;
for (var i=2; i<=s.length; i++) inv[i] = inv[MOD % i] * (MOD - Math.floor(MOD/i));
fakt[0] = 1; fakt[1] = 1;
rev_fakt[0] = 1; rev_fakt[1] = 1;
for (var i=2; i<=s.length; i++) {
	fakt[i] = mulmod(fakt[i-1],i);
	rev_fakt[i] = mulmod(rev_fakt[i-1], inv[i]);
}

var glob_rev = 1;
for (var i=0; i<52; i++)
	if (cnt[i] > 0)
		glob_rev = mulmod(rev_fakt[cnt[i]],glob_rev);

var solve_one = Array(52).fill(-1);

var solve_two = Array(52);
for (var j=0; j<52; j++)
	if (cnt[j] > 0) {
		var tt = Array(52).fill(-1);
		solve_two[j] = tt;
	}

var ee = [];

for (var i=0; i<qq; i++) {
	var a,b;
	var numbers = readline().split(" ").map(function(x) { return parseInt(x); });
	a = numbers[0]-1;
	b = numbers[1]-1;
	var a_ind = get_ind(s[a]);
	var b_ind = get_ind(s[b]);

	var total = cnt[a_ind] + cnt[b_ind];
	if (a_ind === b_ind)
		total -= cnt[b_ind];

	if (total > half) {
		ee.push(0);
		continue;
	}

	if (a_ind > b_ind) a_ind = b_ind + (b_ind=a_ind, 0);   // swap

	if (a_ind !== b_ind) {
		if (solve_two[a_ind][b_ind] === -1) {
			var tt = [];
			for (var k=0; k<52; k++)
				if (k !== a_ind && k !== b_ind && cnt[k] > 0)
					tt.push(cnt[k]);
			solve_two[a_ind][b_ind] = solve(tt);
		}
		ans = mulmod(mulmod(cnk(half, cnt[a_ind]), cnk(half - cnt[a_ind], cnt[b_ind]))*2, fakt[half]);
		ans = mulmod(mulmod(ans, fakt[half-cnt[a_ind]-cnt[b_ind]]), (glob_rev));
		ans = mulmod(mulmod(mulmod(ans,fakt[cnt[a_ind]]), fakt[cnt[b_ind]]), solve_two[a_ind][b_ind]);
	}
	else {
		if (solve_one[a_ind] === -1) {
			var tt = [];
			for (var j=0; j<52; j++)
				if (j !== a_ind && cnt[j] > 0)
					tt.push(cnt[j]);
			solve_one[a_ind] = solve(tt);
		}
		ans = mulmod(mulmod(mulmod(mulmod(mulmod(cnk(half, cnt[a_ind]), fakt[half])*2, fakt[half-cnt[a_ind]]), glob_rev), fakt[cnt[a_ind]]), solve_one[a_ind]);
	}
	ee.push(ans);
}

print(ee.join("\n"));

;(function (globalObject) {
  'use strict';

  var BigNumber,
    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
    mathceil = Math.ceil,
    mathfloor = Math.floor,
    bignumberError = '[BigNumber Error] ',
    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
    BASE = 1e14,
    LOG_BASE = 14,
    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
    SQRT_BASE = 1e7,
    MAX = 1E9;                                   // 0 to MAX_INT32

  function clone(configObject) {
    var div, convertBase, parseNumeric,
      P = BigNumber.prototype = { constructor: BigNumber, toString: null, valueOf: null },
      ONE = new BigNumber(1),

      // The maximum number of decimal places for operations involving division.
      DECIMAL_PLACES = 1000,                   // 0 to MAX
      ROUNDING_MODE = 1,                       // 0 to 8 (look at ROUND_)

      // The exponent value at and beneath which toString returns exponential notation.
      TO_EXP_NEG = -1000,                      // 0 to -MAX
      // The exponent value at and above which toString returns exponential notation.
      TO_EXP_POS = 1000,                       // 0 to MAX
      MIN_EXP = -1e8,                          // -1 to -MAX
      MAX_EXP = 1e8,                           // 1 to MAX

      CRYPTO = false,                          // true or false
      MODULO_MODE = 1,                         // 0 to 9
      POW_PRECISION = 0,                       // 0 to MAX
      FORMAT = {
        prefix: '',
        groupSize: 3,
        secondaryGroupSize: 0,
        groupSeparator: ',',
        decimalSeparator: '.',
        fractionGroupSize: 0,
        fractionGroupSeparator: '\xA0',      // non-breaking space
        suffix: ''
      },
      ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';

    function BigNumber(n, b) {
      var alphabet, c, caseChanged, e, i, isNum, len, str,
        x = this;
      if (!(x instanceof BigNumber)) {
        return new BigNumber(n, b);
      }
      if (b == null) {
        if (n instanceof BigNumber) {
          x.s = n.s;
          x.e = n.e;
          x.c = (n = n.c) ? n.slice() : n;
          return;
        }
        isNum = typeof n == 'number';
        if (isNum && n * 0 == 0) {
          x.s = 1 / n < 0 ? (n = -n, -1) : 1;
          if (n === ~~n) {
            for (e = 0, i = n; i >= 10; i /= 10, e++);
            x.e = e;
            x.c = [n];
            return;
          }
          str = String(n);
        } else {
          str = String(n);
          if (!isNumeric.test(str)) return parseNumeric(x, str, isNum);
          x.s = str.charCodeAt(0) == 45 ? (str = str.slice(1), -1) : 1;
        }
        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
        if ((i = str.search(/e/i)) > 0) {
          if (e < 0) e = i;
          e += +str.slice(i + 1);
          str = str.substring(0, i);
        } else if (e < 0) {
          e = str.length;
        }
      } else {
        intCheck(b, 2, ALPHABET.length, 'Base');
        str = String(n);
        if (b == 10) {
          x = new BigNumber(n instanceof BigNumber ? n : str);
          return round(x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE);
        }
        isNum = typeof n == 'number';
        if (isNum) {
          if (n * 0 != 0) return parseNumeric(x, str, isNum, b);
          x.s = 1 / n < 0 ? (str = str.slice(1), -1) : 1;
          if (BigNumber.DEBUG && str.replace(/^0\.0*|\./, '').length > 15) {
            throw Error
             (tooManyDigits + n);
          }
          isNum = false;
        } else {
          x.s = str.charCodeAt(0) === 45 ? (str = str.slice(1), -1) : 1;
        }
        alphabet = ALPHABET.slice(0, b);
        e = i = 0;
        for (len = str.length; i < len; i++) {
          if (alphabet.indexOf(c = str.charAt(i)) < 0) {
            if (c == '.') {
              if (i > e) {
                e = len;
                continue;
              }
            } else if (!caseChanged) {
              if (str == str.toUpperCase() && (str = str.toLowerCase()) ||
                  str == str.toLowerCase() && (str = str.toUpperCase())) {
                caseChanged = true;
                i = -1;
                e = 0;
                continue;
              }
            }
            return parseNumeric(x, String(n), isNum, b);
          }
        }
        str = convertBase(str, b, 10, x.s);
        if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
        else e = str.length;
      }
      for (i = 0; str.charCodeAt(i) === 48; i++);
      for (len = str.length; str.charCodeAt(--len) === 48;);
      str = str.slice(i, ++len);
      if (str) {
        len -= i;
        if (isNum && BigNumber.DEBUG &&
          len > 15 && (n > MAX_SAFE_INTEGER || n !== mathfloor(n))) {
            throw Error
             (tooManyDigits + (x.s * n));
        }
        e = e - i - 1;
        if (e > MAX_EXP) {
          x.c = x.e = null;
        } else if (e < MIN_EXP) {
          x.c = [x.e = 0];
        } else {
          x.e = e;
          x.c = [];
          i = (e + 1) % LOG_BASE;
          if (e < 0) i += LOG_BASE;
          if (i < len) {
            if (i) x.c.push(+str.slice(0, i));
            for (len -= LOG_BASE; i < len;) {
              x.c.push(+str.slice(i, i += LOG_BASE));
            }
            str = str.slice(i);
            i = LOG_BASE - str.length;
          } else {
            i -= len;
          }
          for (; i--; str += '0');
          x.c.push(+str);
        }
      } else {
        x.c = [x.e = 0];
      }
    }

    BigNumber.clone = clone;
    BigNumber.ROUND_UP = 0;
    BigNumber.ROUND_DOWN = 1;
    BigNumber.ROUND_CEIL = 2;
    BigNumber.ROUND_FLOOR = 3;
    BigNumber.ROUND_HALF_UP = 4;
    BigNumber.ROUND_HALF_DOWN = 5;
    BigNumber.ROUND_HALF_EVEN = 6;
    BigNumber.ROUND_HALF_CEIL = 7;
    BigNumber.ROUND_HALF_FLOOR = 8;
    BigNumber.EUCLID = 9;

    BigNumber.config = BigNumber.set = function (obj) {
      var p, v;
      if (obj != null) {
        if (typeof obj == 'object') {
          if (obj.hasOwnProperty(p = 'DECIMAL_PLACES')) {
            v = obj[p];
            intCheck(v, 0, MAX, p);
            DECIMAL_PLACES = v;
          }
          if (obj.hasOwnProperty(p = 'ROUNDING_MODE')) {
            v = obj[p];
            intCheck(v, 0, 8, p);
            ROUNDING_MODE = v;
          }
          if (obj.hasOwnProperty(p = 'EXPONENTIAL_AT')) {
            v = obj[p];
            if (v && v.pop) {
              intCheck(v[0], -MAX, 0, p);
              intCheck(v[1], 0, MAX, p);
              TO_EXP_NEG = v[0];
              TO_EXP_POS = v[1];
            } else {
              intCheck(v, -MAX, MAX, p);
              TO_EXP_NEG = -(TO_EXP_POS = v < 0 ? -v : v);
            }
          }
          if (obj.hasOwnProperty(p = 'RANGE')) {
            v = obj[p];
            if (v && v.pop) {
              intCheck(v[0], -MAX, -1, p);
              intCheck(v[1], 1, MAX, p);
              MIN_EXP = v[0];
              MAX_EXP = v[1];
            } else {
              intCheck(v, -MAX, MAX, p);
              if (v) {
                MIN_EXP = -(MAX_EXP = v < 0 ? -v : v);
              } else {
                throw Error
                 (bignumberError + p + ' cannot be zero: ' + v);
              }
            }
          }
          if (obj.hasOwnProperty(p = 'CRYPTO')) {
            v = obj[p];
            if (v === !!v) {
              if (v) {
                if (typeof crypto != 'undefined' && crypto &&
                 (crypto.getRandomValues || crypto.randomBytes)) {
                  CRYPTO = v;
                } else {
                  CRYPTO = !v;
                  throw Error
                   (bignumberError + 'crypto unavailable');
                }
              } else {
                CRYPTO = v;
              }
            } else {
              throw Error
               (bignumberError + p + ' not true or false: ' + v);
            }
          }
          if (obj.hasOwnProperty(p = 'MODULO_MODE')) {
            v = obj[p];
            intCheck(v, 0, 9, p);
            MODULO_MODE = v;
          }
          if (obj.hasOwnProperty(p = 'POW_PRECISION')) {
            v = obj[p];
            intCheck(v, 0, MAX, p);
            POW_PRECISION = v;
          }
          if (obj.hasOwnProperty(p = 'FORMAT')) {
            v = obj[p];
            if (typeof v == 'object') FORMAT = v;
            else throw Error
             (bignumberError + p + ' not an object: ' + v);
          }
          if (obj.hasOwnProperty(p = 'ALPHABET')) {
            v = obj[p];
            if (typeof v == 'string' && !/^.$|[+-.\s]|(.).*\1/.test(v)) {
              ALPHABET = v;
            } else {
              throw Error
               (bignumberError + p + ' invalid: ' + v);
            }
          }
        } else {
          throw Error
           (bignumberError + 'Object expected: ' + obj);
        }
      }

      return {
        DECIMAL_PLACES: DECIMAL_PLACES,
        ROUNDING_MODE: ROUNDING_MODE,
        EXPONENTIAL_AT: [TO_EXP_NEG, TO_EXP_POS],
        RANGE: [MIN_EXP, MAX_EXP],
        CRYPTO: CRYPTO,
        MODULO_MODE: MODULO_MODE,
        POW_PRECISION: POW_PRECISION,
        FORMAT: FORMAT,
        ALPHABET: ALPHABET
      };
    };

    BigNumber.isBigNumber = function (v) {
      return v instanceof BigNumber || v && v._isBigNumber === true || false;
    };

    BigNumber.maximum = BigNumber.max = function () {
      return maxOrMin(arguments, P.lt);
    };

    BigNumber.minimum = BigNumber.min = function () {
      return maxOrMin(arguments, P.gt);
    };

    BigNumber.random = (function () {
      var pow2_53 = 0x20000000000000;
      var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
       ? function () { return mathfloor(Math.random() * pow2_53); }
       : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
         (Math.random() * 0x800000 | 0); };
      return function (dp) {
        var a, b, e, k, v,
          i = 0,
          c = [],
          rand = new BigNumber(ONE);
        if (dp == null) dp = DECIMAL_PLACES;
        else intCheck(dp, 0, MAX);
        k = mathceil(dp / LOG_BASE);
        if (CRYPTO) {
          if (crypto.getRandomValues) {
            a = crypto.getRandomValues(new Uint32Array(k *= 2));
            for (; i < k;) {
              v = a[i] * 0x20000 + (a[i + 1] >>> 11);
              if (v >= 9e15) {
                b = crypto.getRandomValues(new Uint32Array(2));
                a[i] = b[0];
                a[i + 1] = b[1];
              } else {
                c.push(v % 1e14);
                i += 2;
              }
            }
            i = k / 2;
          } else if (crypto.randomBytes) {
            a = crypto.randomBytes(k *= 7);
            for (; i < k;) {
              v = ((a[i] & 31) * 0x1000000000000) + (a[i + 1] * 0x10000000000) +
                 (a[i + 2] * 0x100000000) + (a[i + 3] * 0x1000000) +
                 (a[i + 4] << 16) + (a[i + 5] << 8) + a[i + 6];
              if (v >= 9e15) {
                crypto.randomBytes(7).copy(a, i);
              } else {
                c.push(v % 1e14);
                i += 7;
              }
            }
            i = k / 7;
          } else {
            CRYPTO = false;
            throw Error
             (bignumberError + 'crypto unavailable');
          }
        }
        if (!CRYPTO) {
          for (; i < k;) {
            v = random53bitInt();
            if (v < 9e15) c[i++] = v % 1e14;
          }
        }
        k = c[--i];
        dp %= LOG_BASE;
        if (k && dp) {
          v = POWS_TEN[LOG_BASE - dp];
          c[i] = mathfloor(k / v) * v;
        }
        for (; c[i] === 0; c.pop(), i--);
        if (i < 0) {
          c = [e = 0];
        } else {
          for (e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
          for (i = 1, v = c[0]; v >= 10; v /= 10, i++);
          if (i < LOG_BASE) e -= LOG_BASE - i;
        }
        rand.e = e;
        rand.c = c;
        return rand;
      };
    })();

    BigNumber.sum = function () {
      var i = 1,
        args = arguments,
        sum = new BigNumber(args[0]);
      for (; i < args.length;) sum = sum.plus(args[i++]);
      return sum;
    };

    convertBase = (function () {
      var decimal = '0123456789';
      function toBaseOut(str, baseIn, baseOut, alphabet) {
        var j,
          arr = [0],
          arrL,
          i = 0,
          len = str.length;
        for (; i < len;) {
          for (arrL = arr.length; arrL--; arr[arrL] *= baseIn);
          arr[0] += alphabet.indexOf(str.charAt(i++));
          for (j = 0; j < arr.length; j++) {
            if (arr[j] > baseOut - 1) {
              if (arr[j + 1] == null) arr[j + 1] = 0;
              arr[j + 1] += arr[j] / baseOut | 0;
              arr[j] %= baseOut;
            }
          }
        }
        return arr.reverse();
      }
      return function (str, baseIn, baseOut, sign, callerIsToString) {
        var alphabet, d, e, k, r, x, xc, y,
          i = str.indexOf('.'),
          dp = DECIMAL_PLACES,
          rm = ROUNDING_MODE;
        if (i >= 0) {
          k = POW_PRECISION;
          POW_PRECISION = 0;
          str = str.replace('.', '');
          y = new BigNumber(baseIn);
          x = y.pow(str.length - i);
          POW_PRECISION = k;
          y.c = toBaseOut(toFixedPoint(coeffToString(x.c), x.e, '0'),
           10, baseOut, decimal);
          y.e = y.c.length;
        }
        xc = toBaseOut(str, baseIn, baseOut, callerIsToString
         ? (alphabet = ALPHABET, decimal)
         : (alphabet = decimal, ALPHABET));
        e = k = xc.length;
        for (; xc[--k] == 0; xc.pop());
        if (!xc[0]) return alphabet.charAt(0);
        if (i < 0) {
          --e;
        } else {
          x.c = xc;
          x.e = e;
          x.s = sign;
          x = div(x, y, dp, rm, baseOut);
          xc = x.c;
          r = x.r;
          e = x.e;
        }
        d = e + dp + 1;
        i = xc[d];
        k = baseOut / 2;
        r = r || d < 0 || xc[d + 1] != null;
        r = rm < 4 ? (i != null || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
              : i > k || i == k &&(rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
               rm == (x.s < 0 ? 8 : 7));
        if (d < 1 || !xc[0]) {
          str = r ? toFixedPoint(alphabet.charAt(1), -dp, alphabet.charAt(0)) : alphabet.charAt(0);
        } else {
          xc.length = d;
          if (r) {
            for (--baseOut; ++xc[--d] > baseOut;) {
              xc[d] = 0;
              if (!d) {
                ++e;
                xc = [1].concat(xc);
              }
            }
          }
          for (k = xc.length; !xc[--k];);
          for (i = 0, str = ''; i <= k; str += alphabet.charAt(xc[i++]));
          str = toFixedPoint(str, e, alphabet.charAt(0));
        }
        return str;
      };
    })();

    div = (function () {
      function multiply(x, k, base) {
        var m, temp, xlo, xhi,
          carry = 0,
          i = x.length,
          klo = k % SQRT_BASE,
          khi = k / SQRT_BASE | 0;
        for (x = x.slice(); i--;) {
          xlo = x[i] % SQRT_BASE;
          xhi = x[i] / SQRT_BASE | 0;
          m = khi * xlo + xhi * klo;
          temp = klo * xlo + ((m % SQRT_BASE) * SQRT_BASE) + carry;
          carry = (temp / base | 0) + (m / SQRT_BASE | 0) + khi * xhi;
          x[i] = temp % base;
        }
        if (carry) x = [carry].concat(x);
        return x;
      }

      function compare(a, b, aL, bL) {
        var i, cmp;
        if (aL != bL) {
          cmp = aL > bL ? 1 : -1;
        } else {
          for (i = cmp = 0; i < aL; i++) {
            if (a[i] != b[i]) {
              cmp = a[i] > b[i] ? 1 : -1;
              break;
            }
          }
        }
        return cmp;
      }

      function subtract(a, b, aL, base) {
        var i = 0;
        for (; aL--;) {
          a[aL] -= i;
          i = a[aL] < b[aL] ? 1 : 0;
          a[aL] = i * base + a[aL] - b[aL];
        }
        for (; !a[0] && a.length > 1; a.splice(0, 1));
      }
      return function (x, y, dp, rm, base) {
        var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
          yL, yz,
          s = x.s == y.s ? 1 : -1,
          xc = x.c,
          yc = y.c;
        if (!xc || !xc[0] || !yc || !yc[0]) {
          return new BigNumber(
           !x.s || !y.s || (xc ? yc && xc[0] == yc[0] : !yc) ? NaN :
            xc && xc[0] == 0 || !yc ? s * 0 : s / 0
         );
        }
        q = new BigNumber(s);
        qc = q.c = [];
        e = x.e - y.e;
        s = dp + e + 1;
        if (!base) {
          base = BASE;
          e = bitFloor(x.e / LOG_BASE) - bitFloor(y.e / LOG_BASE);
          s = s / LOG_BASE | 0;
        }
        for (i = 0; yc[i] == (xc[i] || 0); i++);
        if (yc[i] > (xc[i] || 0)) e--;
        if (s < 0) {
          qc.push(1);
          more = true;
        } else {
          xL = xc.length;
          yL = yc.length;
          i = 0;
          s += 2;
          n = mathfloor(base / (yc[0] + 1));
          if (n > 1) {
            yc = multiply(yc, n, base);
            xc = multiply(xc, n, base);
            yL = yc.length;
            xL = xc.length;
          }
          xi = yL;
          rem = xc.slice(0, yL);
          remL = rem.length;
          for (; remL < yL; rem[remL++] = 0);
          yz = yc.slice();
          yz = [0].concat(yz);
          yc0 = yc[0];
          if (yc[1] >= base / 2) yc0++;
          do {
            n = 0;
            cmp = compare(yc, rem, yL, remL);
            if (cmp < 0) {
              rem0 = rem[0];
              if (yL != remL) rem0 = rem0 * base + (rem[1] || 0);
              n = mathfloor(rem0 / yc0);
              if (n > 1) {
                if (n >= base) n = base - 1;
                prod = multiply(yc, n, base);
                prodL = prod.length;
                remL = rem.length;
                while (compare(prod, rem, prodL, remL) == 1) {
                  n--;
                  subtract(prod, yL < prodL ? yz : yc, prodL, base);
                  prodL = prod.length;
                  cmp = 1;
                }
              } else {
                if (n == 0) {
                  cmp = n = 1;
                }
                prod = yc.slice();
                prodL = prod.length;
              }
              if (prodL < remL) prod = [0].concat(prod);
              subtract(rem, prod, remL, base);
              remL = rem.length;
              if (cmp == -1) {
                while (compare(yc, rem, yL, remL) < 1) {
                  n++;
                  subtract(rem, yL < remL ? yz : yc, remL, base);
                  remL = rem.length;
                }
              }
            } else if (cmp === 0) {
              n++;
              rem = [0];
            }
            qc[i++] = n;
            if (rem[0]) {
              rem[remL++] = xc[xi] || 0;
            } else {
              rem = [xc[xi]];
              remL = 1;
            }
          } while ((xi++ < xL || rem[0] != null) && s--);
          more = rem[0] != null;
          if (!qc[0]) qc.splice(0, 1);
        }
        if (base == BASE) {
          for (i = 1, s = qc[0]; s >= 10; s /= 10, i++);
          round(q, dp + (q.e = i + e * LOG_BASE - 1) + 1, rm, more);
        } else {
          q.e = e;
          q.r = +more;
        }
        return q;
      };
    })();

    function format(n, i, rm, id) {
      var c0, e, ne, len, str;
      if (rm == null) rm = ROUNDING_MODE;
      else intCheck(rm, 0, 8);
      if (!n.c) return n.toString();
      c0 = n.c[0];
      ne = n.e;
      if (i == null) {
        str = coeffToString(n.c);
        str = id == 1 || id == 2 && (ne <= TO_EXP_NEG || ne >= TO_EXP_POS)
         ? toExponential(str, ne)
         : toFixedPoint(str, ne, '0');
      } else {
        n = round(new BigNumber(n), i, rm);
        e = n.e;
        str = coeffToString(n.c);
        len = str.length;
        if (id == 1 || id == 2 && (i <= e || e <= TO_EXP_NEG)) {
          for (; len < i; str += '0', len++);
          str = toExponential(str, e);
        } else {
          i -= ne;
          str = toFixedPoint(str, e, '0');
          if (e + 1 > len) {
            if (--i > 0) for (str += '.'; i--; str += '0');
          } else {
            i += e - len;
            if (i > 0) {
              if (e + 1 == len) str += '.';
              for (; i--; str += '0');
            }
          }
        }
      }
      return n.s < 0 && c0 ? '-' + str : str;
    }

    function maxOrMin(args, method) {
      var n,
        i = 1,
        m = new BigNumber(args[0]);
      for (; i < args.length; i++) {
        n = new BigNumber(args[i]);
        if (!n.s) {
          m = n;
          break;
        } else if (method.call(m, n)) {
          m = n;
        }
      }
      return m;
    }

    function normalise(n, c, e) {
      var i = 1,
        j = c.length;
      for (; !c[--j]; c.pop());
      for (j = c[0]; j >= 10; j /= 10, i++);
      if ((e = i + e * LOG_BASE - 1) > MAX_EXP) {
        n.c = n.e = null;
      } else if (e < MIN_EXP) {
        n.c = [n.e = 0];
      } else {
        n.e = e;
        n.c = c;
      }
      return n;
    }

    parseNumeric = (function () {
      var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
        dotAfter = /^([^.]+)\.$/,
        dotBefore = /^\.([^.]+)$/,
        isInfinityOrNaN = /^-?(Infinity|NaN)$/,
        whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
      return function (x, str, isNum, b) {
        var base,
          s = isNum ? str : str.replace(whitespaceOrPlus, '');
        if (isInfinityOrNaN.test(s)) {
          x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
          x.c = x.e = null;
        } else {
          if (!isNum) {
            s = s.replace(basePrefix, function (m, p1, p2) {
              base = (p2 = p2.toLowerCase()) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
              return !b || b == base ? p1 : m;
            });
            if (b) {
              base = b;
              s = s.replace(dotAfter, '$1').replace(dotBefore, '0.$1');
            }
            if (str != s) return new BigNumber(s, base);
          }
          if (BigNumber.DEBUG) {
            throw Error
              (bignumberError + 'Not a' + (b ? ' base ' + b : '') + ' number: ' + str);
          }
          x.c = x.e = x.s = null;
        }
      }
    })();

    function round(x, sd, rm, r) {
      var d, i, j, k, n, ni, rd,
        xc = x.c,
        pows10 = POWS_TEN;
      if (xc) {
        out: {
          for (d = 1, k = xc[0]; k >= 10; k /= 10, d++);
          i = sd - d;
          if (i < 0) {
            i += LOG_BASE;
            j = sd;
            n = xc[ni = 0];
            rd = n / pows10[d - j - 1] % 10 | 0;
          } else {
            ni = mathceil((i + 1) / LOG_BASE);
            if (ni >= xc.length) {
              if (r) {
                for (; xc.length <= ni; xc.push(0));
                n = rd = 0;
                d = 1;
                i %= LOG_BASE;
                j = i - LOG_BASE + 1;
              } else {
                break out;
              }
            } else {
              n = k = xc[ni];
              for (d = 1; k >= 10; k /= 10, d++);
              i %= LOG_BASE;
              j = i - LOG_BASE + d;
              rd = j < 0 ? 0 : n / pows10[d - j - 1] % 10 | 0;
            }
          }
          r = r || sd < 0 ||
           xc[ni + 1] != null || (j < 0 ? n : n % pows10[d - j - 1]);
          r = rm < 4
           ? (rd || r) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
           : rd > 5 || rd == 5 && (rm == 4 || r || rm == 6 &&
            ((i > 0 ? j > 0 ? n / pows10[d - j] : 0 : xc[ni - 1]) % 10) & 1 ||
             rm == (x.s < 0 ? 8 : 7));
          if (sd < 1 || !xc[0]) {
            xc.length = 0;
            if (r) {
              sd -= x.e + 1;
              xc[0] = pows10[(LOG_BASE - sd % LOG_BASE) % LOG_BASE];
              x.e = -sd || 0;
            } else {
              xc[0] = x.e = 0;
            }
            return x;
          }
          if (i == 0) {
            xc.length = ni;
            k = 1;
            ni--;
          } else {
            xc.length = ni + 1;
            k = pows10[LOG_BASE - i];
            xc[ni] = j > 0 ? mathfloor(n / pows10[d - j] % pows10[j]) * k : 0;
          }
          if (r) {
            for (; ;) {
              if (ni == 0) {
                for (i = 1, j = xc[0]; j >= 10; j /= 10, i++);
                j = xc[0] += k;
                for (k = 1; j >= 10; j /= 10, k++);
                if (i != k) {
                  x.e++;
                  if (xc[0] == BASE) xc[0] = 1;
                }
                break;
              } else {
                xc[ni] += k;
                if (xc[ni] != BASE) break;
                xc[ni--] = 0;
                k = 1;
              }
            }
          }
          for (i = xc.length; xc[--i] === 0; xc.pop());
        }
        if (x.e > MAX_EXP) {
          x.c = x.e = null;
        } else if (x.e < MIN_EXP) {
          x.c = [x.e = 0];
        }
      }
      return x;
    }

    function valueOf(n) {
      var str,
        e = n.e;
      if (e === null) return n.toString();
      str = coeffToString(n.c);
      str = e <= TO_EXP_NEG || e >= TO_EXP_POS
        ? toExponential(str, e)
        : toFixedPoint(str, e, '0');
      return n.s < 0 ? '-' + str : str;
    }

    P.absoluteValue = P.abs = function () {
      var x = new BigNumber(this);
      if (x.s < 0) x.s = 1;
      return x;
    };

    P.comparedTo = function (y, b) {
      return compare(this, new BigNumber(y, b));
    };

    P.decimalPlaces = P.dp = function (dp, rm) {
      var c, n, v,
        x = this;
      if (dp != null) {
        intCheck(dp, 0, MAX);
        if (rm == null) rm = ROUNDING_MODE;
        else intCheck(rm, 0, 8);
        return round(new BigNumber(x), dp + x.e + 1, rm);
      }
      if (!(c = x.c)) return null;
      n = ((v = c.length - 1) - bitFloor(this.e / LOG_BASE)) * LOG_BASE;
      if (v = c[v]) for (; v % 10 == 0; v /= 10, n--);
      if (n < 0) n = 0;
      return n;
    };

    P.dividedBy = P.div = function (y, b) {
      return div(this, new BigNumber(y, b), DECIMAL_PLACES, ROUNDING_MODE);
    };

    P.dividedToIntegerBy = P.idiv = function (y, b) {
      return div(this, new BigNumber(y, b), 0, 1);
    };

    P.exponentiatedBy = P.pow = function (n, m) {
      var half, isModExp, i, k, more, nIsBig, nIsNeg, nIsOdd, y,
        x = this;
      n = new BigNumber(n);
      if (n.c && !n.isInteger()) {
        throw Error
          (bignumberError + 'Exponent not an integer: ' + valueOf(n));
      }
      if (m != null) m = new BigNumber(m);
      nIsBig = n.e > 14;
      if (!x.c || !x.c[0] || x.c[0] == 1 && !x.e && x.c.length == 1 || !n.c || !n.c[0]) {
        y = new BigNumber(Math.pow(+valueOf(x), nIsBig ? 2 - isOdd(n) : +valueOf(n)));
        return m ? y.mod(m) : y;
      }
      nIsNeg = n.s < 0;
      if (m) {
        if (m.c ? !m.c[0] : !m.s) return new BigNumber(NaN);
        isModExp = !nIsNeg && x.isInteger() && m.isInteger();
        if (isModExp) x = x.mod(m);
      } else if (n.e > 9 && (x.e > 0 || x.e < -1 || (x.e == 0
        ? x.c[0] > 1 || nIsBig && x.c[1] >= 24e7
        : x.c[0] < 8e13 || nIsBig && x.c[0] <= 9999975e7))) {
        k = x.s < 0 && isOdd(n) ? -0 : 0;
        if (x.e > -1) k = 1 / k;
        return new BigNumber(nIsNeg ? 1 / k : k);
      } else if (POW_PRECISION) {
        k = mathceil(POW_PRECISION / LOG_BASE + 2);
      }
      if (nIsBig) {
        half = new BigNumber(0.5);
        if (nIsNeg) n.s = 1;
        nIsOdd = isOdd(n);
      } else {
        i = Math.abs(+valueOf(n));
        nIsOdd = i % 2;
      }
      y = new BigNumber(ONE);
      for (; ;) {
        if (nIsOdd) {
          y = y.times(x);
          if (!y.c) break;

          if (k) {
            if (y.c.length > k) y.c.length = k;
          } else if (isModExp) {
            y = y.mod(m);
          }
        }
        if (i) {
          i = mathfloor(i / 2);
          if (i === 0) break;
          nIsOdd = i % 2;
        } else {
          n = n.times(half);
          round(n, n.e + 1, 1);
          if (n.e > 14) {
            nIsOdd = isOdd(n);
          } else {
            i = +valueOf(n);
            if (i === 0) break;
            nIsOdd = i % 2;
          }
        }
        x = x.times(x);
        if (k) {
          if (x.c && x.c.length > k) x.c.length = k;
        } else if (isModExp) {
          x = x.mod(m);
        }
      }
      if (isModExp) return y;
      if (nIsNeg) y = ONE.div(y);
      return m ? y.mod(m) : k ? round(y, POW_PRECISION, ROUNDING_MODE, more) : y;
    };

    P.integerValue = function (rm) {
      var n = new BigNumber(this);
      if (rm == null) rm = ROUNDING_MODE;
      else intCheck(rm, 0, 8);
      return round(n, n.e + 1, rm);
    };

    P.isEqualTo = P.eq = function (y, b) {
      return compare(this, new BigNumber(y, b)) === 0;
    };

    P.isFinite = function () {
      return !!this.c;
    };

    P.isGreaterThan = P.gt = function (y, b) {
      return compare(this, new BigNumber(y, b)) > 0;
    };

    P.isGreaterThanOrEqualTo = P.gte = function (y, b) {
      return (b = compare(this, new BigNumber(y, b))) === 1 || b === 0;

    };

    P.isInteger = function () {
      return !!this.c && bitFloor(this.e / LOG_BASE) > this.c.length - 2;
    };

    P.isLessThan = P.lt = function (y, b) {
      return compare(this, new BigNumber(y, b)) < 0;
    };

    P.isLessThanOrEqualTo = P.lte = function (y, b) {
      return (b = compare(this, new BigNumber(y, b))) === -1 || b === 0;
    };

    P.isNaN = function () {
      return !this.s;
    };

    P.isNegative = function () {
      return this.s < 0;
    };

    P.isPositive = function () {
      return this.s > 0;
    };

    P.isZero = function () {
      return !!this.c && this.c[0] == 0;
    };

    P.minus = function (y, b) {
      var i, j, t, xLTy,
        x = this,
        a = x.s;
      y = new BigNumber(y, b);
      b = y.s;
      if (!a || !b) return new BigNumber(NaN);
      if (a != b) {
        y.s = -b;
        return x.plus(y);
      }
      var xe = x.e / LOG_BASE,
        ye = y.e / LOG_BASE,
        xc = x.c,
        yc = y.c;
      if (!xe || !ye) {
        if (!xc || !yc) return xc ? (y.s = -b, y) : new BigNumber(yc ? x : NaN);
        if (!xc[0] || !yc[0]) {
          return yc[0] ? (y.s = -b, y) : new BigNumber(xc[0] ? x :
           ROUNDING_MODE == 3 ? -0 : 0);
        }
      }
      xe = bitFloor(xe);
      ye = bitFloor(ye);
      xc = xc.slice();
      if (a = xe - ye) {
        if (xLTy = a < 0) {
          a = -a;
          t = xc;
        } else {
          ye = xe;
          t = yc;
        }
        t.reverse();
        for (b = a; b--; t.push(0));
        t.reverse();
      } else {
        j = (xLTy = (a = xc.length) < (b = yc.length)) ? a : b;
        for (a = b = 0; b < j; b++) {
          if (xc[b] != yc[b]) {
            xLTy = xc[b] < yc[b];
            break;
          }
        }
      }
      if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
      b = (j = yc.length) - (i = xc.length);
      if (b > 0) for (; b--; xc[i++] = 0);
      b = BASE - 1;
      for (; j > a;) {
        if (xc[--j] < yc[j]) {
          for (i = j; i && !xc[--i]; xc[i] = b);
          --xc[i];
          xc[j] += BASE;
        }

        xc[j] -= yc[j];
      }
      for (; xc[0] == 0; xc.splice(0, 1), --ye);
      if (!xc[0]) {
        y.s = ROUNDING_MODE == 3 ? -1 : 1;
        y.c = [y.e = 0];
        return y;
      }
      return normalise(y, xc, ye);
    };

    P.modulo = P.mod = function (y, b) {
      var q, s,
        x = this;
      y = new BigNumber(y, b);
      if (!x.c || !y.s || y.c && !y.c[0]) {
        return new BigNumber(NaN);
      } else if (!y.c || x.c && !x.c[0]) {
        return new BigNumber(x);
      }
      if (MODULO_MODE == 9) {
        s = y.s;
        y.s = 1;
        q = div(x, y, 0, 3);
        y.s = s;
        q.s *= s;
      } else {
        q = div(x, y, 0, MODULO_MODE);
      }
      y = x.minus(q.times(y));
      if (!y.c[0] && MODULO_MODE == 1) y.s = x.s;
      return y;
    };

    P.multipliedBy = P.times = function (y, b) {
      var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
        base, sqrtBase,
        x = this,
        xc = x.c,
        yc = (y = new BigNumber(y, b)).c;
      if (!xc || !yc || !xc[0] || !yc[0]) {
        if (!x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc) {
          y.c = y.e = y.s = null;
        } else {
          y.s *= x.s;
          if (!xc || !yc) {
            y.c = y.e = null;
          } else {
            y.c = [0];
            y.e = 0;
          }
        }
        return y;
      }
      e = bitFloor(x.e / LOG_BASE) + bitFloor(y.e / LOG_BASE);
      y.s *= x.s;
      xcL = xc.length;
      ycL = yc.length;
      if (xcL < ycL) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
      for (i = xcL + ycL, zc = []; i--; zc.push(0));
      base = BASE;
      sqrtBase = SQRT_BASE;
      for (i = ycL; --i >= 0;) {
        c = 0;
        ylo = yc[i] % sqrtBase;
        yhi = yc[i] / sqrtBase | 0;
        for (k = xcL, j = i + k; j > i;) {
          xlo = xc[--k] % sqrtBase;
          xhi = xc[k] / sqrtBase | 0;
          m = yhi * xlo + xhi * ylo;
          xlo = ylo * xlo + ((m % sqrtBase) * sqrtBase) + zc[j] + c;
          c = (xlo / base | 0) + (m / sqrtBase | 0) + yhi * xhi;
          zc[j--] = xlo % base;
        }
        zc[j] = c;
      }
      if (c) {
        ++e;
      } else {
        zc.splice(0, 1);
      }
      return normalise(y, zc, e);
    };

    P.negated = function () {
      var x = new BigNumber(this);
      x.s = -x.s || null;
      return x;
    };

    P.plus = function (y, b) {
      var t,
        x = this,
        a = x.s;
      y = new BigNumber(y, b);
      b = y.s;
      if (!a || !b) return new BigNumber(NaN);
       if (a != b) {
        y.s = -b;
        return x.minus(y);
      }
      var xe = x.e / LOG_BASE,
        ye = y.e / LOG_BASE,
        xc = x.c,
        yc = y.c;
      if (!xe || !ye) {
        if (!xc || !yc) return new BigNumber(a / 0);
        if (!xc[0] || !yc[0]) return yc[0] ? y : new BigNumber(xc[0] ? x : a * 0);
      }
      xe = bitFloor(xe);
      ye = bitFloor(ye);
      xc = xc.slice();
      if (a = xe - ye) {
        if (a > 0) {
          ye = xe;
          t = yc;
        } else {
          a = -a;
          t = xc;
        }
        t.reverse();
        for (; a--; t.push(0));
        t.reverse();
      }
      a = xc.length;
      b = yc.length;
      if (a - b < 0) t = yc, yc = xc, xc = t, b = a;
      for (a = 0; b;) {
        a = (xc[--b] = xc[b] + yc[b] + a) / BASE | 0;
        xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
      }
      if (a) {
        xc = [a].concat(xc);
        ++ye;
      }
      return normalise(y, xc, ye);
    };

    P.precision = P.sd = function (sd, rm) {
      var c, n, v,
        x = this;
      if (sd != null && sd !== !!sd) {
        intCheck(sd, 1, MAX);
        if (rm == null) rm = ROUNDING_MODE;
        else intCheck(rm, 0, 8);
        return round(new BigNumber(x), sd, rm);
      }
      if (!(c = x.c)) return null;
      v = c.length - 1;
      n = v * LOG_BASE + 1;
      if (v = c[v]) {
        for (; v % 10 == 0; v /= 10, n--);
        for (v = c[0]; v >= 10; v /= 10, n++);
      }
      if (sd && x.e + 1 > n) n = x.e + 1;
      return n;
    };
    P.shiftedBy = function (k) {
      intCheck(k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
      return this.times('1e' + k);
    };
    P.squareRoot = P.sqrt = function () {
      var m, n, r, rep, t,
        x = this,
        c = x.c,
        s = x.s,
        e = x.e,
        dp = DECIMAL_PLACES + 4,
        half = new BigNumber('0.5');
      if (s !== 1 || !c || !c[0]) {
        return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
      }
      s = Math.sqrt(+valueOf(x));
      if (s == 0 || s == 1 / 0) {
        n = coeffToString(c);
        if ((n.length + e) % 2 == 0) n += '0';
        s = Math.sqrt(+n);
        e = bitFloor((e + 1) / 2) - (e < 0 || e % 2);

        if (s == 1 / 0) {
          n = '1e' + e;
        } else {
          n = s.toExponential();
          n = n.slice(0, n.indexOf('e') + 1) + e;
        }
        r = new BigNumber(n);
      } else {
        r = new BigNumber(s + '');
      }
      if (r.c[0]) {
        e = r.e;
        s = e + dp;
        if (s < 3) s = 0;
        for (; ;) {
          t = r;
          r = half.times(t.plus(div(x, t, dp, 1)));
          if (coeffToString(t.c).slice(0, s) === (n = coeffToString(r.c)).slice(0, s)) {
            if (r.e < e) --s;
            n = n.slice(s - 3, s + 1);
            if (n == '9999' || !rep && n == '4999') {
              if (!rep) {
                round(t, t.e + DECIMAL_PLACES + 2, 0);

                if (t.times(t).eq(x)) {
                  r = t;
                  break;
                }
              }
              dp += 4;
              s += 4;
              rep = 1;
            } else {
              if (!+n || !+n.slice(1) && n.charAt(0) == '5') {
                round(r, r.e + DECIMAL_PLACES + 2, 1);
                m = !r.times(r).eq(x);
              }
              break;
            }
          }
        }
      }

      return round(r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m);
    };

    P.toExponential = function (dp, rm) {
      if (dp != null) {
        intCheck(dp, 0, MAX);
        dp++;
      }
      return format(this, dp, rm, 1);
    };

    P.toFixed = function (dp, rm) {
      if (dp != null) {
        intCheck(dp, 0, MAX);
        dp = dp + this.e + 1;
      }
      return format(this, dp, rm);
    };

    P.toFormat = function (dp, rm, format) {
      var str,
        x = this;

      if (format == null) {
        if (dp != null && rm && typeof rm == 'object') {
          format = rm;
          rm = null;
        } else if (dp && typeof dp == 'object') {
          format = dp;
          dp = rm = null;
        } else {
          format = FORMAT;
        }
      } else if (typeof format != 'object') {
        throw Error
          (bignumberError + 'Argument not an object: ' + format);
      }

      str = x.toFixed(dp, rm);

      if (x.c) {
        var i,
          arr = str.split('.'),
          g1 = +format.groupSize,
          g2 = +format.secondaryGroupSize,
          groupSeparator = format.groupSeparator || '',
          intPart = arr[0],
          fractionPart = arr[1],
          isNeg = x.s < 0,
          intDigits = isNeg ? intPart.slice(1) : intPart,
          len = intDigits.length;

        if (g2) i = g1, g1 = g2, g2 = i, len -= i;

        if (g1 > 0 && len > 0) {
          i = len % g1 || g1;
          intPart = intDigits.substr(0, i);
          for (; i < len; i += g1) intPart += groupSeparator + intDigits.substr(i, g1);
          if (g2 > 0) intPart += groupSeparator + intDigits.slice(i);
          if (isNeg) intPart = '-' + intPart;
        }

        str = fractionPart
         ? intPart + (format.decimalSeparator || '') + ((g2 = +format.fractionGroupSize)
          ? fractionPart.replace(new RegExp('\\d{' + g2 + '}\\B', 'g'),
           '$&' + (format.fractionGroupSeparator || ''))
          : fractionPart)
         : intPart;
      }

      return (format.prefix || '') + str + (format.suffix || '');
    };

    P.toFraction = function (md) {
      var d, d0, d1, d2, e, exp, n, n0, n1, q, r, s,
        x = this,
        xc = x.c;

      if (md != null) {
        n = new BigNumber(md);
        if (!n.isInteger() && (n.c || n.s !== 1) || n.lt(ONE)) {
          throw Error
            (bignumberError + 'Argument ' +
              (n.isInteger() ? 'out of range: ' : 'not an integer: ') + valueOf(n));
        }
      }

      if (!xc) return new BigNumber(x);

      d = new BigNumber(ONE);
      n1 = d0 = new BigNumber(ONE);
      d1 = n0 = new BigNumber(ONE);
      s = coeffToString(xc);

      e = d.e = s.length - x.e - 1;
      d.c[0] = POWS_TEN[(exp = e % LOG_BASE) < 0 ? LOG_BASE + exp : exp];
      md = !md || n.comparedTo(d) > 0 ? (e > 0 ? d : n1) : n;

      exp = MAX_EXP;
      MAX_EXP = 1 / 0;
      n = new BigNumber(s);
      n0.c[0] = 0;

      for (; ;)  {
        q = div(n, d, 0, 1);
        d2 = d0.plus(q.times(d1));
        if (d2.comparedTo(md) == 1) break;
        d0 = d1;
        d1 = d2;
        n1 = n0.plus(q.times(d2 = n1));
        n0 = d2;
        d = n.minus(q.times(d2 = d));
        n = d2;
      }

      d2 = div(md.minus(d0), d1, 0, 1);
      n0 = n0.plus(d2.times(n1));
      d0 = d0.plus(d2.times(d1));
      n0.s = n1.s = x.s;
      e = e * 2;

      r = div(n1, d1, e, ROUNDING_MODE).minus(x).abs().comparedTo(
          div(n0, d0, e, ROUNDING_MODE).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0];
      MAX_EXP = exp;

      return r;
    };

    P.toNumber = function () {
      return +valueOf(this);
    };

    P.toPrecision = function (sd, rm) {
      if (sd != null) intCheck(sd, 1, MAX);
      return format(this, sd, rm, 2);
    };

    P.toString = function (b) {
      var str,
        n = this,
        s = n.s,
        e = n.e;

      if (e === null) {
        if (s) {
          str = 'Infinity';
          if (s < 0) str = '-' + str;
        } else {
          str = 'NaN';
        }
      } else {
        if (b == null) {
          str = e <= TO_EXP_NEG || e >= TO_EXP_POS
           ? toExponential(coeffToString(n.c), e)
           : toFixedPoint(coeffToString(n.c), e, '0');
        } else if (b === 10) {
          n = round(new BigNumber(n), DECIMAL_PLACES + e + 1, ROUNDING_MODE);
          str = toFixedPoint(coeffToString(n.c), n.e, '0');
        } else {
          intCheck(b, 2, ALPHABET.length, 'Base');
          str = convertBase(toFixedPoint(coeffToString(n.c), e, '0'), 10, b, s, true);
        }

        if (s < 0 && n.c[0]) str = '-' + str;
      }

      return str;
    };

    P.valueOf = P.toJSON = function () {
      return valueOf(this);
    };

    P._isBigNumber = true;
    if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') {
      P[Symbol.toStringTag] = 'BigNumber';
      P[Symbol.for('nodejs.util.inspect.custom')] = P.valueOf;
    }
    if (configObject != null) BigNumber.set(configObject);
    return BigNumber;
  }

  function bitFloor(n) {
    var i = n | 0;
    return n > 0 || n === i ? i : i - 1;
  }

  function coeffToString(a) {
    var s, z,
      i = 1,
      j = a.length,
      r = a[0] + '';
    for (; i < j;) {
      s = a[i++] + '';
      z = LOG_BASE - s.length;
      for (; z--; s = '0' + s);
      r += s;
    }
    for (j = r.length; r.charCodeAt(--j) === 48;);
    return r.slice(0, j + 1 || 1);
  }

  function compare(x, y) {
    var a, b,
      xc = x.c,
      yc = y.c,
      i = x.s,
      j = y.s,
      k = x.e,
      l = y.e;
    if (!i || !j) return null;
    a = xc && !xc[0];
    b = yc && !yc[0];
    if (a || b) return a ? b ? 0 : -j : i;
    if (i != j) return i;
    a = i < 0;
    b = k == l;
    if (!xc || !yc) return b ? 0 : !xc ^ a ? 1 : -1;
    if (!b) return k > l ^ a ? 1 : -1;
    j = (k = xc.length) < (l = yc.length) ? k : l;
    for (i = 0; i < j; i++) if (xc[i] != yc[i]) return xc[i] > yc[i] ^ a ? 1 : -1;
    return k == l ? 0 : k > l ^ a ? 1 : -1;
  }

  function intCheck(n, min, max, name) {
    if (n < min || n > max || n !== (n < 0 ? mathceil(n) : mathfloor(n))) {
      throw Error
       (bignumberError + (name || 'Argument') + (typeof n == 'number'
         ? n < min || n > max ? ' out of range: ' : ' not an integer: '
         : ' not a primitive number: ') + String(n));
    }
  }

  function isOdd(n) {
    var k = n.c.length - 1;
    return bitFloor(n.e / LOG_BASE) == k && n.c[k] % 2 != 0;
  }

  function toExponential(str, e) {
    return (str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str) +
     (e < 0 ? 'e' : 'e+') + e;
  }

  function toFixedPoint(str, e, z) {
    var len, zs;
    if (e < 0) {
      for (zs = z + '.'; ++e; zs += z);
      str = zs + str;
    } else {
      len = str.length;
      if (++e > len) {
        for (zs = z, e -= len; --e; zs += z);
        str += zs;
      } else if (e < len) {
        str = str.slice(0, e) + '.' + str.slice(e);
      }
    }
    return str;
  }

  BigNumber = clone();
  BigNumber['default'] = BigNumber.BigNumber = BigNumber;
  if (typeof define == 'function' && define.amd) {
    define(function () { return BigNumber; });
  } else if (typeof module != 'undefined' && module.exports) {
    module.exports = BigNumber;
  } else {
    if (!globalObject) {
      globalObject = typeof self != 'undefined' && self ? self : window;
    }
    globalObject.BigNumber = BigNumber;
  }
})(this);

//var qq = readline().split(" ").map(function(x) { return parseInt(x); });
var s = readline();
var qq = readline().split(" ").map(function(x) { return parseInt(x); })[0];

var cnt = Array(52).fill(0);
const ALPHABET = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ';

get_ind = function (c) {
 	return ALPHABET.indexOf(c);
};

var MODULE = new BigNumber(1000000007);

find_deg = function(x, deg, MODULE) {
	var b = 1, a = x;
	while (deg > 0) {
		if (deg % 2 === 1)
			b = Number(BigNumber(b).times(a).mod(MODULE));
		deg = Math.floor(deg / 2);
		if (deg > 0)
			a = Number(BigNumber(a).times(a).mod(MODULE));
	}
	return Number(b);
};

find_rev = function(x, MODULE) {
	return find_deg(x, MODULE-2, MODULE);
};

var fakt = Array(s.length+1).fill(0);
var rev_fakt = Array(s.length+1).fill(0);

cnk = function(n, k) {
	return Number(BigNumber(fakt[n]).times(rev_fakt[k]).times(rev_fakt[n-k]).mod(MODULE));
}

for (var i=0; i<s.length; i++)
	cnt[get_ind(s[i])]++;

var half = Math.floor(s.length / 2);

var ans = new BigNumber(0);
var total_ans = 0;

fakt[0] = 1; fakt[1] = 1;
for (var i=2; i<=s.length; i++)
	fakt[i] = Number(BigNumber(fakt[i-1]).times(i).mod(MODULE));

rev_fakt[0] = 1; rev_fakt[1] = 1;
rev_fakt[s.length] = find_rev(fakt[s.length], MODULE);
for (var i = s.length - 1; i > 1; i--)
	rev_fakt[i] = Number(BigNumber(rev_fakt[i+1]).times(i+1).mod(MODULE));

var glob_rev = 1;
for (var i=0; i<52; i++)
	if (cnt[i] > 0)
		glob_rev = Number(BigNumber(rev_fakt[cnt[i]]).times(glob_rev).mod(MODULE));

//print(fakt);
//print(rev_fakt);

for (var i=0; i<qq; i++) {
	var a,b;
	var numbers = readline().split(" ").map(function(x) { return parseInt(x); });
	a = numbers[0]-1;
	b = numbers[1]-1;
	var a_ind = get_ind(s[a]);
	var b_ind = get_ind(s[b]);

	var total = cnt[a_ind] + cnt[b_ind];
	if (a_ind === b_ind)
		total -= cnt[b_ind];

	if (total > half) {
		print("0");
		continue;
	}

	if (a_ind !== b_ind)
		ans = BigNumber(cnk(half, cnt[a_ind])).times(cnk(half - cnt[a_ind], cnt[b_ind])).times(2).times(glob_rev).times(fakt[cnt[a_ind]]).times(fakt[cnt[b_ind]]).times(fakt[half*2-cnt[a_ind]-cnt[b_ind]]).mod(MODULE);
	else
		ans = BigNumber(cnk(half, cnt[a_ind])).times(2).times(glob_rev).times(fakt[cnt[a_ind]]).times(fakt[half*2-cnt[a_ind]]).mod(MODULE);
	print(Number(ans));
}