The length of the longest common prefix of two strings $$$s=s_1 s_2 \ldots s_n$$$ and $$$t = t_1 t_2 \ldots t_m$$$ is defined as the maximum $$$k \le \min(n, m)$$$ such that $$$s_1 s_2 \ldots s_k$$$ equals $$$t_1 t_2 \ldots t_k$$$. Let's denote the longest common prefix of two strings $$$s$$$ and $$$t$$$ as $$$lcp(s,t)$$$.Z-function of a string $$$s_1 s_2 \dots s_n$$$ is a sequence of integers $$$z_1, z_2, \ldots, z_n$$$, where $$$z_i = lcp(s_1 s_2 \ldots s_n,\ \ s_i s_{i+1} \dots s_n)$$$. Ж-function of a string $$$s$$$ is defined as $$$z_1 + z_2 + \ldots + z_n$$$.You're given a string $$$s=s_1 s_2 \ldots s_n$$$ and $$$q$$$ queries. Each query is described by two integers $$$l_i$$$ and $$$r_i$$$, where $$$1 \le l_i \le r_i \le n$$$. The answer for the query is defined as Ж-function of the string $$$s_{l_i} s_{l_i +1} \ldots s_{r_i}$$$.

The first line contains the string $$$s$$$, consisting of lowercase English letters ($$$1 \leq |s| \leq 200\,000$$$). The second line contains one integer $$$q$$$ — the number of queries ($$$1 \leq q \leq 200\,000$$$). Each of the following $$$q$$$ lines contains two integers $$$l_i$$$ and $$$r_i$$$, describing the query ($$$1 \leq l_i \leq r_i \leq |s|$$$).

For every query output one integer: the value of Ж-function of the corresponding substring.

NoteIn the first sample case there are four queries:  the first query corresponds to the substring bb, and its Ж-function equals $$$2 + 1 = 3$$$; the second query corresponds to the substring abb, and its Ж-function equals $$$3 + 0 + 0 = 3$$$; the third query corresponds to the substring b, and its Ж-function equals $$$1$$$. the fourth query corresponds to the substring abdd, and its Ж-function equals $$$4 + 0 + 0 + 0= 4$$$.


Andrey received a postcard from Irina. It contained only the words "Hello, Andrey!", and a strange string consisting of lowercase Latin letters, snowflakes and candy canes. Andrey thought that this string is an encrypted message, and decided to decrypt it.Andrey noticed that snowflakes and candy canes always stand after the letters, so he supposed that the message was encrypted as follows. Candy cane means that the letter before it can be removed, or can be left. A snowflake means that the letter before it can be removed, left, or repeated several times.For example, consider the following string:   This string can encode the message «happynewyear». For this, candy canes and snowflakes should be used as follows:   candy cane 1: remove the letter w,  snowflake 1: repeat the letter p twice,  candy cane 2: leave the letter n,  snowflake 2: remove the letter w,  snowflake 3: leave the letter e.   Please note that the same string can encode different messages. For example, the string above can encode «hayewyar», «happpppynewwwwwyear», and other messages.Andrey knows that messages from Irina usually have a length of $$$k$$$ letters. Help him to find out if a given string can encode a message of $$$k$$$ letters, and if so, give an example of such a message.

The first line contains the string received in the postcard. The string consists only of lowercase Latin letters, as well as the characters «*» and «?», meaning snowflake and candy cone, respectively. These characters can only appear immediately after the letter. The length of the string does not exceed $$$200$$$. The second line contains an integer number $$$k$$$ ($$$1 \leq k \leq 200$$$), the required message length.

Print any message of length $$$k$$$ that the given string can encode, or «Impossible» if such a message does not exist.


NN is an experienced internet user and that means he spends a lot of time on the social media. Once he found the following image on the Net, which asked him to compare the sizes of inner circles:  It turned out that the circles are equal. NN was very surprised by this fact, so he decided to create a similar picture himself.He managed to calculate the number of outer circles $$$n$$$ and the radius of the inner circle $$$r$$$. NN thinks that, using this information, you can exactly determine the radius of the outer circles $$$R$$$ so that the inner circle touches all of the outer ones externally and each pair of neighboring outer circles also touches each other. While NN tried very hard to guess the required radius, he didn't manage to do that. Help NN find the required radius for building the required picture.

The first and the only line of the input file contains two numbers $$$n$$$ and $$$r$$$ ($$$3 \leq n \leq 100$$$, $$$1 \leq r \leq 100$$$) — the number of the outer circles and the radius of the inner circle respectively.

Output a single number $$$R$$$ — the radius of the outer circle required for building the required picture.  Your answer will be accepted if its relative or absolute error does not exceed $$$10^{-6}$$$. Formally, if your answer is $$$a$$$ and the jury's answer is $$$b$$$. Your answer is accepted if and only when $$$\frac{|a-b|}{max(1, |b|)} \le 10^{-6}$$$.


This is an interactive task.Dasha and NN like playing chess. While playing a match they decided that normal chess isn't interesting enough for them, so they invented a game described below.There are $$$666$$$ black rooks and $$$1$$$ white king on the chess board of size $$$999 \times 999$$$. The white king wins if he gets checked by rook, or, in other words, if he moves onto the square which shares either a row or column with a black rook.The sides take turns, starting with white. NN plays as a white king and on each of his turns he moves a king to one of the squares that are adjacent to his current position either by side or diagonally, or, formally, if the king was on the square $$$(x, y)$$$, it can move to the square $$$(nx, ny)$$$ if and only $$$\max (|nx - x|, |ny - y|) = 1$$$ , $$$1 \leq nx, ny \leq 999$$$. NN is also forbidden from moving onto the squares occupied with black rooks, however, he can move onto the same row or column as a black rook.Dasha, however, neglects playing by the chess rules, and instead of moving rooks normally she moves one of her rooks on any space devoid of other chess pieces. It is also possible that the rook would move onto the same square it was before and the position wouldn't change. However, she can't move the rook on the same row or column with the king.Each player makes $$$2000$$$ turns, if the white king wasn't checked by a black rook during those turns, black wins. NN doesn't like losing, but thinks the task is too difficult for him, so he asks you to write a program that will always win playing for the white king. Note that Dasha can see your king and play depending on its position.

In the beginning your program will receive $$$667$$$ lines from input. Each line contains two integers $$$x$$$ and $$$y$$$ ($$$1 \leq x, y \leq 999$$$) — the piece's coordinates. The first line contains the coordinates of the king and the next $$$666$$$ contain the coordinates of the rooks. The first coordinate denotes the number of the row where the piece is located, the second denotes the column. It is guaranteed that initially the king isn't in check and that all pieces occupy different squares.

After getting king checked, you program should terminate immediately without printing anything extra.

NoteThe example is trimmed. The full initial positions of the rooks in the first test are available at https://pastebin.com/qQCTXgKP. It is not guaranteed that they will behave as in the example.


Andrew prefers taxi to other means of transport, but recently most taxi drivers have been acting inappropriately. In order to earn more money, taxi drivers started to drive in circles. Roads in Andrew's city are one-way, and people are not necessary able to travel from one part to another, but it pales in comparison to insidious taxi drivers.The mayor of the city decided to change the direction of certain roads so that the taxi drivers wouldn't be able to increase the cost of the trip endlessly. More formally, if the taxi driver is on a certain crossroads, they wouldn't be able to reach it again if he performs a nonzero trip. Traffic controllers are needed in order to change the direction the road goes. For every road it is known how many traffic controllers are needed to change the direction of the road to the opposite one. It is allowed to change the directions of roads one by one, meaning that each traffic controller can participate in reversing two or more roads.You need to calculate the minimum number of traffic controllers that you need to hire to perform the task and the list of the roads that need to be reversed.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \leq n \leq 100\,000$$$, $$$1 \leq m \leq 100\,000$$$) — the number of crossroads and the number of roads in the city, respectively. Each of the following $$$m$$$ lines contain three integers $$$u_{i}$$$, $$$v_{i}$$$ and $$$c_{i}$$$ ($$$1 \leq u_{i}, v_{i} \leq n$$$, $$$1 \leq c_{i} \leq 10^9$$$, $$$u_{i} \ne v_{i}$$$) — the crossroads the road starts at, the crossroads the road ends at and the number of traffic controllers required to reverse this road.

In the first line output two integers the minimal amount of traffic controllers required to complete the task and amount of roads $$$k$$$ which should be reversed. $$$k$$$ should not be minimized. In the next line output $$$k$$$ integers separated by spaces — numbers of roads, the directions of which should be reversed. The roads are numerated from $$$1$$$ in the order they are written in the input. If there are many solutions, print any of them.

NoteThere are two simple cycles in the first example: $$$1 \rightarrow 5 \rightarrow 2 \rightarrow 1$$$ and $$$2 \rightarrow 3 \rightarrow 4 \rightarrow 5 \rightarrow 2$$$. One traffic controller can only reverse the road $$$2 \rightarrow 1$$$ and he can't destroy the second cycle by himself. Two traffic controllers can reverse roads $$$2 \rightarrow 1$$$ and $$$2 \rightarrow 3$$$ which would satisfy the condition.In the second example one traffic controller can't destroy the cycle $$$ 1 \rightarrow 3 \rightarrow 2 \rightarrow 1 $$$. With the help of three controllers we can, for example, reverse roads $$$1 \rightarrow 3$$$ ,$$$ 2 \rightarrow 4$$$, $$$1 \rightarrow 5$$$.


Ivan loves burgers and spending money. There are $$$n$$$ burger joints on the street where Ivan lives. Ivan has $$$q$$$ friends, and the $$$i$$$-th friend suggested to meet at the joint $$$l_i$$$ and walk to the joint $$$r_i$$$ $$$(l_i \leq r_i)$$$. While strolling with the $$$i$$$-th friend Ivan can visit all joints $$$x$$$ which satisfy $$$l_i \leq x \leq r_i$$$.For each joint Ivan knows the cost of the most expensive burger in it, it costs $$$c_i$$$ burles. Ivan wants to visit some subset of joints on his way, in each of them he will buy the most expensive burger and spend the most money. But there is a small issue: his card broke and instead of charging him for purchases, the amount of money on it changes as follows.If Ivan had $$$d$$$ burles before the purchase and he spent $$$c$$$ burles at the joint, then after the purchase he would have $$$d \oplus c$$$ burles, where $$$\oplus$$$ denotes the bitwise XOR operation.Currently Ivan has $$$2^{2^{100}} - 1$$$ burles and he wants to go out for a walk. Help him to determine the maximal amount of burles he can spend if he goes for a walk with the friend $$$i$$$. The amount of burles he spends is defined as the difference between the initial amount on his account and the final account.

The first line contains one integer $$$n$$$ ($$$1 \leq n \leq 500\,000$$$) — the number of burger shops. The next line contains $$$n$$$ integers $$$c_1, c_2, \ldots, c_n$$$ ($$$0 \leq c_i \leq 10^6$$$), where $$$c_i$$$ — the cost of the most expensive burger in the burger joint $$$i$$$. The third line contains one integer $$$q$$$ ($$$1 \leq q \leq 500\,000$$$) — the number of Ivan's friends. Each of the next $$$q$$$ lines contain two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \leq l_i \leq r_i \leq n$$$) — pairs of numbers of burger shops between which Ivan will walk.

Output $$$q$$$ lines, $$$i$$$-th of which containing the maximum amount of money Ivan can spend with the friend $$$i$$$.

NoteIn the first test, in order to spend the maximum amount of money with the first and third friends, Ivan just needs to go into the first burger. With a second friend, Ivan just go to the third burger.In the second test for a third friend (who is going to walk from the first to the third burger), there are only 8 options to spend money — $$$0$$$, $$$12$$$, $$$14$$$, $$$23$$$, $$$12 \oplus 14 = 2$$$, $$$14 \oplus 23 = 25$$$, $$$12 \oplus 23 = 27$$$, $$$12 \oplus 14 \oplus 23 = 20$$$. The maximum amount of money it turns out to spend, if you go to the first and third burger — $$$12 \oplus 23 = 27$$$.


An accordion is a string (yes, in the real world accordions are musical instruments, but let's forget about it for a while) which can be represented as a concatenation of: an opening bracket (ASCII code $$$091$$$), a colon (ASCII code $$$058$$$), some (possibly zero) vertical line characters (ASCII code $$$124$$$), another colon, and a closing bracket (ASCII code $$$093$$$). The length of the accordion is the number of characters in it.For example, [::], [:||:] and [:|||:] are accordions having length $$$4$$$, $$$6$$$ and $$$7$$$. (:|:), {:||:}, [:], ]:||:[ are not accordions. You are given a string $$$s$$$. You want to transform it into an accordion by removing some (possibly zero) characters from it. Note that you may not insert new characters or reorder existing ones. Is it possible to obtain an accordion by removing characters from $$$s$$$, and if so, what is the maximum possible length of the result?

The only line contains one string $$$s$$$ ($$$1 \le |s| \le 500000$$$). It consists of lowercase Latin letters and characters [, ], : and |.

If it is not possible to obtain an accordion by removing some characters from $$$s$$$, print $$$-1$$$. Otherwise print maximum possible length of the resulting accordion.


There are $$$n$$$ segments $$$[l_i, r_i]$$$ for $$$1 \le i \le n$$$. You should divide all segments into two non-empty groups in such way that there is no pair of segments from different groups which have at least one common point, or say that it's impossible to do it. Each segment should belong to exactly one group.To optimize testing process you will be given multitest.

The first line contains one integer $$$T$$$ ($$$1 \le T \le 50000$$$) — the number of queries. Each query contains description of the set of segments. Queries are independent. First line of each query contains single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — number of segments. It is guaranteed that $$$\sum{n}$$$ over all queries does not exceed $$$10^5$$$. The next $$$n$$$ lines contains two integers $$$l_i$$$, $$$r_i$$$ per line ($$$1 \le l_i \le r_i \le 2 \cdot 10^5$$$) — the $$$i$$$-th segment.

For each query print $$$n$$$ integers $$$t_1, t_2, \dots, t_n$$$ ($$$t_i \in \{1, 2\}$$$) — for each segment (in the same order as in the input) $$$t_i$$$ equals $$$1$$$ if the $$$i$$$-th segment will belongs to the first group and $$$2$$$ otherwise. If there are multiple answers, you can print any of them. If there is no answer, print $$$-1$$$.

NoteIn the first query the first and the second segments should be in different groups, but exact numbers don't matter.In the second query the third segment intersects with the first and the second segments, so they should be in the same group, but then the other group becomes empty, so answer is $$$-1$$$.In the third query we can distribute segments in any way that makes groups non-empty, so any answer of $$$6$$$ possible is correct.


Polycarp has recently got himself a new job. He now earns so much that his old wallet can't even store all the money he has.Berland bills somehow come in lots of different sizes. However, all of them are shaped as rectangles (possibly squares). All wallets are also produced in form of rectangles (possibly squares).A bill $$$x \times y$$$ fits into some wallet $$$h \times w$$$ if either $$$x \le h$$$ and $$$y \le w$$$ or $$$y \le h$$$ and $$$x \le w$$$. Bills can overlap with each other in a wallet and an infinite amount of bills can fit into a wallet. That implies that all the bills Polycarp currently have fit into a wallet if every single one of them fits into it independently of the others.Now you are asked to perform the queries of two types:  $$$+~x~y$$$ — Polycarp earns a bill of size $$$x \times y$$$;  $$$?~h~w$$$ — Polycarp wants to check if all the bills he has earned to this moment fit into a wallet of size $$$h \times w$$$. It is guaranteed that there is at least one query of type $$$1$$$ before the first query of type $$$2$$$ and that there is at least one query of type $$$2$$$ in the input data.For each query of type $$$2$$$ print "YES" if all the bills he has earned to this moment fit into a wallet of given size. Print "NO" otherwise.

The first line contains a single integer $$$n$$$ ($$$2 \le n \le 5 \cdot 10^5$$$) — the number of queries. Each of the next $$$n$$$ lines contains a query of one of these two types:   $$$+~x~y$$$ ($$$1 \le x, y \le 10^9$$$) — Polycarp earns a bill of size $$$x \times y$$$;  $$$?~h~w$$$ ($$$1 \le h, w \le 10^9$$$) — Polycarp wants to check if all the bills he has earned to this moment fit into a wallet of size $$$h \times w$$$.  It is guaranteed that there is at least one query of type $$$1$$$ before the first query of type $$$2$$$ and that there is at least one query of type $$$2$$$ in the input data.

NoteThe queries of type $$$2$$$ of the example:  Neither bill fits;  Both bills fit (just checking that you got that bills can overlap);  Both bills fit (both bills are actually the same);  All bills fit (too much of free space in a wallet is not a problem);  Only bill $$$1 \times 5$$$ fit (all the others don't, thus it's "NO").


You are given a tree consisting of $$$n$$$ vertices. A number is written on each vertex; the number on vertex $$$i$$$ is equal to $$$a_i$$$.Let's denote the function $$$g(x, y)$$$ as the greatest common divisor of the numbers written on the vertices belonging to the simple path from vertex $$$x$$$ to vertex $$$y$$$ (including these two vertices). Also let's denote $$$dist(x, y)$$$ as the number of vertices on the simple path between vertices $$$x$$$ and $$$y$$$, including the endpoints. $$$dist(x, x) = 1$$$ for every vertex $$$x$$$.Your task is calculate the maximum value of $$$dist(x, y)$$$ among such pairs of vertices that $$$g(x, y) > 1$$$.

The first line contains one integer $$$n$$$ — the number of vertices $$$(1 \le n \le 2 \cdot 10^5)$$$. The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ $$$(1 \le a_i \le 2 \cdot 10^5)$$$ — the numbers written on vertices. Then $$$n - 1$$$ lines follow, each containing two integers $$$x$$$ and $$$y$$$ $$$(1 \le x, y \le n, x \ne y)$$$ denoting an edge connecting vertex $$$x$$$ with vertex $$$y$$$. It is guaranteed that these edges form a tree.

If there is no pair of vertices $$$x, y$$$ such that $$$g(x, y) > 1$$$, print $$$0$$$. Otherwise print the maximum value of $$$dist(x, y)$$$ among such pairs.


There are $$$n$$$ cities along the road, which can be represented as a straight line. The $$$i$$$-th city is situated at the distance of $$$a_i$$$ kilometers from the origin. All cities are situated in the same direction from the origin. There are $$$m$$$ trucks travelling from one city to another. Each truck can be described by $$$4$$$ integers: starting city $$$s_i$$$, finishing city $$$f_i$$$, fuel consumption $$$c_i$$$ and number of possible refuelings $$$r_i$$$. The $$$i$$$-th truck will spend $$$c_i$$$ litres of fuel per one kilometer. When a truck arrives in some city, it can be refueled (but refueling is impossible in the middle of nowhere). The $$$i$$$-th truck can be refueled at most $$$r_i$$$ times. Each refueling makes truck's gas-tank full. All trucks start with full gas-tank.All trucks will have gas-tanks of the same size $$$V$$$ litres. You should find minimum possible $$$V$$$ such that all trucks can reach their destinations without refueling more times than allowed.

First line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 400$$$, $$$1 \le m \le 250000$$$) — the number of cities and trucks. The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$, $$$a_i < a_{i+1}$$$) — positions of cities in the ascending order. Next $$$m$$$ lines contains $$$4$$$ integers each. The $$$i$$$-th line contains integers $$$s_i$$$, $$$f_i$$$, $$$c_i$$$, $$$r_i$$$ ($$$1 \le s_i < f_i \le n$$$, $$$1 \le c_i \le 10^9$$$, $$$0 \le r_i \le n$$$) — the description of the $$$i$$$-th truck.

Print the only integer — minimum possible size of gas-tanks $$$V$$$ such that all trucks can reach their destinations.

NoteLet's look at queries in details:   the $$$1$$$-st truck must arrive at position $$$7$$$ from $$$2$$$ without refuelling, so it needs gas-tank of volume at least $$$50$$$.  the $$$2$$$-nd truck must arrive at position $$$17$$$ from $$$2$$$ and can be refueled at any city (if it is on the path between starting point and ending point), so it needs gas-tank of volume at least $$$48$$$.  the $$$3$$$-rd truck must arrive at position $$$14$$$ from $$$10$$$, there is no city between, so it needs gas-tank of volume at least $$$52$$$.  the $$$4$$$-th truck must arrive at position $$$17$$$ from $$$10$$$ and can be refueled only one time: it's optimal to refuel at $$$5$$$-th city (position $$$14$$$) so it needs gas-tank of volume at least $$$40$$$.  the $$$5$$$-th truck has the same description, so it also needs gas-tank of volume at least $$$40$$$.  the $$$6$$$-th truck must arrive at position $$$14$$$ from $$$2$$$ and can be refueled two times: first time in city $$$2$$$ or $$$3$$$ and second time in city $$$4$$$ so it needs gas-tank of volume at least $$$55$$$.


You are given an array $$$a_1, a_2, \dots, a_n$$$ of integer numbers.Your task is to divide the array into the maximum number of segments in such a way that:  each element is contained in exactly one segment;  each segment contains at least one element;  there doesn't exist a non-empty subset of segments such that bitwise XOR of the numbers from them is equal to $$$0$$$. Print the maximum number of segments the array can be divided into. Print -1 if no suitable division exists.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of the array. The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^9$$$).

Print the maximum number of segments the array can be divided into while following the given constraints. Print -1 if no suitable division exists.

NoteIn the first example $$$2$$$ is the maximum number. If you divide the array into $$$\{[5], [5, 7, 2]\}$$$, the XOR value of the subset of only the second segment is $$$5 \oplus 7 \oplus 2 = 0$$$. $$$\{[5, 5], [7, 2]\}$$$ has the value of the subset of only the first segment being $$$5 \oplus 5 = 0$$$. However, $$$\{[5, 5, 7], [2]\}$$$ will lead to subsets $$$\{[5, 5, 7]\}$$$ of XOR $$$7$$$, $$$\{[2]\}$$$ of XOR $$$2$$$ and $$$\{[5, 5, 7], [2]\}$$$ of XOR $$$5 \oplus 5 \oplus 7 \oplus 2 = 5$$$.Let's take a look at some division on $$$3$$$ segments — $$$\{[5], [5, 7], [2]\}$$$. It will produce subsets:  $$$\{[5]\}$$$, XOR $$$5$$$;  $$$\{[5, 7]\}$$$, XOR $$$2$$$;  $$$\{[5], [5, 7]\}$$$, XOR $$$7$$$;  $$$\{[2]\}$$$, XOR $$$2$$$;  $$$\{[5], [2]\}$$$, XOR $$$7$$$;  $$$\{[5, 7], [2]\}$$$, XOR $$$0$$$;  $$$\{[5], [5, 7], [2]\}$$$, XOR $$$5$$$; As you can see, subset $$$\{[5, 7], [2]\}$$$ has its XOR equal to $$$0$$$, which is unacceptable. You can check that for other divisions of size $$$3$$$ or $$$4$$$, non-empty subset with $$$0$$$ XOR always exists.The second example has no suitable divisions.The third example array can be divided into $$$\{[3], [1], [10]\}$$$. No subset of these segments has its XOR equal to $$$0$$$.


You are given $$$q$$$ queries in the following form:Given three integers $$$l_i$$$, $$$r_i$$$ and $$$d_i$$$, find minimum positive integer $$$x_i$$$ such that it is divisible by $$$d_i$$$ and it does not belong to the segment $$$[l_i, r_i]$$$.Can you answer all the queries?Recall that a number $$$x$$$ belongs to segment $$$[l, r]$$$ if $$$l \le x \le r$$$.

The first line contains one integer $$$q$$$ ($$$1 \le q \le 500$$$) — the number of queries. Then $$$q$$$ lines follow, each containing a query given in the format $$$l_i$$$ $$$r_i$$$ $$$d_i$$$ ($$$1 \le l_i \le r_i \le 10^9$$$, $$$1 \le d_i \le 10^9$$$). $$$l_i$$$, $$$r_i$$$ and $$$d_i$$$ are integers.

For each query print one integer: the answer to this query.


You are given a string $$$s$$$ consisting of exactly $$$n$$$ characters, and each character is either '0', '1' or '2'. Such strings are called ternary strings.Your task is to replace minimum number of characters in this string with other characters to obtain a balanced ternary string (balanced ternary string is a ternary string such that the number of characters '0' in this string is equal to the number of characters '1', and the number of characters '1' (and '0' obviously) is equal to the number of characters '2').Among all possible balanced ternary strings you have to obtain the lexicographically (alphabetically) smallest.Note that you can neither remove characters from the string nor add characters to the string. Also note that you can replace the given characters only with characters '0', '1' and '2'.It is guaranteed that the answer exists.

The first line of the input contains one integer $$$n$$$ ($$$3 \le n \le 3 \cdot 10^5$$$, $$$n$$$ is divisible by $$$3$$$) — the number of characters in $$$s$$$. The second line contains the string $$$s$$$ consisting of exactly $$$n$$$ characters '0', '1' and '2'.

Print one string — the lexicographically (alphabetically) smallest balanced ternary string which can be obtained from the given one with minimum number of replacements. Because $$$n$$$ is divisible by $$$3$$$ it is obvious that the answer exists. And it is obvious that there is only one possible answer.


You are policeman and you are playing a game with Slavik. The game is turn-based and each turn consists of two phases. During the first phase you make your move and during the second phase Slavik makes his move.There are $$$n$$$ doors, the $$$i$$$-th door initially has durability equal to $$$a_i$$$.During your move you can try to break one of the doors. If you choose door $$$i$$$ and its current durability is $$$b_i$$$ then you reduce its durability to $$$max(0, b_i - x)$$$ (the value $$$x$$$ is given).During Slavik's move he tries to repair one of the doors. If he chooses door $$$i$$$ and its current durability is $$$b_i$$$ then he increases its durability to $$$b_i + y$$$ (the value $$$y$$$ is given). Slavik cannot repair doors with current durability equal to $$$0$$$.The game lasts $$$10^{100}$$$ turns. If some player cannot make his move then he has to skip it.Your goal is to maximize the number of doors with durability equal to $$$0$$$ at the end of the game. You can assume that Slavik wants to minimize the number of such doors. What is the number of such doors in the end if you both play optimally?

The first line of the input contains three integers $$$n$$$, $$$x$$$ and $$$y$$$ ($$$1 \le n \le 100$$$, $$$1 \le x, y \le 10^5$$$) — the number of doors, value $$$x$$$ and value $$$y$$$, respectively. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^5$$$), where $$$a_i$$$ is the initial durability of the $$$i$$$-th door.

Print one integer — the number of doors with durability equal to $$$0$$$ at the end of the game, if you and Slavik both play optimally.

NoteClarifications about the optimal strategy will be ignored.


You are given an array $$$a$$$ consisting of $$$n$$$ integer numbers.You have to color this array in $$$k$$$ colors in such a way that:   Each element of the array should be colored in some color;  For each $$$i$$$ from $$$1$$$ to $$$k$$$ there should be at least one element colored in the $$$i$$$-th color in the array;  For each $$$i$$$ from $$$1$$$ to $$$k$$$ all elements colored in the $$$i$$$-th color should be distinct. Obviously, such coloring might be impossible. In this case, print "NO". Otherwise print "YES" and any coloring (i.e. numbers $$$c_1, c_2, \dots c_n$$$, where $$$1 \le c_i \le k$$$ and $$$c_i$$$ is the color of the $$$i$$$-th element of the given array) satisfying the conditions above. If there are multiple answers, you can print any.

The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 5000$$$) — the length of the array $$$a$$$ and the number of colors, respectively. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 5000$$$) — elements of the array $$$a$$$.

If there is no answer, print "NO". Otherwise print "YES" and any coloring (i.e. numbers $$$c_1, c_2, \dots c_n$$$, where $$$1 \le c_i \le k$$$ and $$$c_i$$$ is the color of the $$$i$$$-th element of the given array) satisfying the conditions described in the problem statement. If there are multiple answers, you can print any.

NoteIn the first example the answer $$$2~ 1~ 2~ 1$$$ is also acceptable.In the second example the answer $$$1~ 1~ 1~ 2~ 2$$$ is also acceptable.There exist other acceptable answers for both examples.


You are given an integer sequence $$$1, 2, \dots, n$$$. You have to divide it into two sets $$$A$$$ and $$$B$$$ in such a way that each element belongs to exactly one set and $$$|sum(A) - sum(B)|$$$ is minimum possible.The value $$$|x|$$$ is the absolute value of $$$x$$$ and $$$sum(S)$$$ is the sum of elements of the set $$$S$$$.

The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^9$$$).

Print one integer — the minimum possible value of $$$|sum(A) - sum(B)|$$$ if you divide the initial sequence $$$1, 2, \dots, n$$$ into two sets $$$A$$$ and $$$B$$$.

NoteSome (not all) possible answers to examples:In the first example you can divide the initial sequence into sets $$$A = \{1, 2\}$$$ and $$$B = \{3\}$$$ so the answer is $$$0$$$.In the second example you can divide the initial sequence into sets $$$A = \{1, 3, 4\}$$$ and $$$B = \{2, 5\}$$$ so the answer is $$$1$$$.In the third example you can divide the initial sequence into sets $$$A = \{1, 4, 5\}$$$ and $$$B = \{2, 3, 6\}$$$ so the answer is $$$1$$$.


You are given an array $$$a$$$ consisting of $$$n$$$ integers. Let's denote monotonic renumeration of array $$$a$$$ as an array $$$b$$$ consisting of $$$n$$$ integers such that all of the following conditions are met:  $$$b_1 = 0$$$;  for every pair of indices $$$i$$$ and $$$j$$$ such that $$$1 \le i, j \le n$$$, if $$$a_i = a_j$$$, then $$$b_i = b_j$$$ (note that if $$$a_i \ne a_j$$$, it is still possible that $$$b_i = b_j$$$);  for every index $$$i \in [1, n - 1]$$$ either $$$b_i = b_{i + 1}$$$ or $$$b_i + 1 = b_{i + 1}$$$. For example, if $$$a = [1, 2, 1, 2, 3]$$$, then two possible monotonic renumerations of $$$a$$$ are $$$b = [0, 0, 0, 0, 0]$$$ and $$$b = [0, 0, 0, 0, 1]$$$.Your task is to calculate the number of different monotonic renumerations of $$$a$$$. The answer may be large, so print it modulo $$$998244353$$$.

The first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of elements in $$$a$$$. The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

Print one integer — the number of different monotonic renumerations of $$$a$$$, taken modulo $$$998244353$$$.


Cardbluff is popular sport game in Telegram. Each Cardbluff player has ever dreamed about entrance in the professional layer. There are $$$n$$$ judges now in the layer and you are trying to pass the entrance exam. You have a number $$$k$$$ — your skill in Cardbluff.Each judge has a number $$$a_i$$$ — an indicator of uncertainty about your entrance to the professional layer and a number $$$e_i$$$ — an experience playing Cardbluff. To pass the exam you need to convince all judges by playing with them. You can play only one game with each judge. As a result of a particular game, you can divide the uncertainty of $$$i$$$-th judge by any natural divisor of $$$a_i$$$ which is at most $$$k$$$. If GCD of all indicators is equal to $$$1$$$, you will enter to the professional layer and become a judge.Also, you want to minimize the total amount of spent time. So, if you play with $$$x$$$ judges with total experience $$$y$$$ you will spend $$$x \cdot y$$$ seconds.Print minimal time to enter to the professional layer or $$$-1$$$ if it's impossible.

There are two numbers in the first line $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 10^6$$$, $$$1 \leq k \leq 10^{12}$$$) — the number of judges and your skill in Cardbluff. The second line contains $$$n$$$ integers, where $$$i$$$-th number $$$a_i$$$ ($$$1 \leq a_i \leq 10^{12}$$$) — the uncertainty of $$$i$$$-th judge The third line contains $$$n$$$ integers in the same format ($$$1 \leq e_i \leq 10^9$$$), $$$e_i$$$ — the experience of $$$i$$$-th judge.

Print the single integer — minimal number of seconds to pass exam, or $$$-1$$$ if it's impossible


Let's define radix sum of number $$$a$$$ consisting of digits $$$a_1, \ldots ,a_k$$$ and number $$$b$$$ consisting of digits $$$b_1, \ldots ,b_k$$$(we add leading zeroes to the shorter number to match longer length) as number $$$s(a,b)$$$ consisting of digits $$$(a_1+b_1)\mod 10, \ldots ,(a_k+b_k)\mod 10$$$. The radix sum of several integers is defined as follows: $$$s(t_1, \ldots ,t_n)=s(t_1,s(t_2, \ldots ,t_n))$$$You are given an array $$$x_1, \ldots ,x_n$$$. The task is to compute for each integer $$$i (0 \le i < n)$$$ number of ways to consequently choose one of the integers from the array $$$n$$$ times, so that the radix sum of these integers is equal to $$$i$$$. Calculate these values modulo $$$2^{58}$$$.

The first line contains integer $$$n$$$ — the length of the array($$$1 \leq n \leq 100000$$$). The second line contains $$$n$$$ integers $$$x_1, \ldots x_n$$$ — array elements($$$0 \leq x_i < 100000$$$).

Output $$$n$$$ integers $$$y_0, \ldots, y_{n-1}$$$ — $$$y_i$$$ should be equal to corresponding number of ways modulo $$$2^{58}$$$.

NoteIn the first example there exist sequences: sequence $$$(5,5)$$$ with radix sum $$$0$$$, sequence $$$(5,6)$$$ with radix sum $$$1$$$, sequence $$$(6,5)$$$ with radix sum $$$1$$$, sequence $$$(6,6)$$$ with radix sum $$$2$$$.


You are given a matrix $$$a$$$, consisting of $$$n$$$ rows and $$$m$$$ columns. Each cell contains an integer in it.You can change the order of rows arbitrarily (including leaving the initial order), but you can't change the order of cells in a row. After you pick some order of rows, you traverse the whole matrix the following way: firstly visit all cells of the first column from the top row to the bottom one, then the same for the second column and so on. During the traversal you write down the sequence of the numbers on the cells in the same order you visited them. Let that sequence be $$$s_1, s_2, \dots, s_{nm}$$$. The traversal is $$$k$$$-acceptable if for all $$$i$$$ ($$$1 \le i \le nm - 1$$$) $$$|s_i - s_{i + 1}| \ge k$$$.Find the maximum integer $$$k$$$ such that there exists some order of rows of matrix $$$a$$$ that it produces a $$$k$$$-acceptable traversal.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 16$$$, $$$1 \le m \le 10^4$$$, $$$2 \le nm$$$) — the number of rows and the number of columns, respectively. Each of the next $$$n$$$ lines contains $$$m$$$ integers ($$$1 \le a_{i, j} \le 10^9$$$) — the description of the matrix.

Print a single integer $$$k$$$ — the maximum number such that there exists some order of rows of matrix $$$a$$$ that it produces an $$$k$$$-acceptable traversal.

NoteIn the first example you can rearrange rows as following to get the $$$5$$$-acceptable traversal:5 310 84 39 9Then the sequence $$$s$$$ will be $$$[5, 10, 4, 9, 3, 8, 3, 9]$$$. Each pair of neighbouring elements have at least $$$k = 5$$$ difference between them.In the second example the maximum $$$k = 0$$$, any order is $$$0$$$-acceptable.In the third example the given order is already $$$3$$$-acceptable, you can leave it as it is.


You are given a 4x4 grid. You play a game — there is a sequence of tiles, each of them is either 2x1 or 1x2. Your task is to consequently place all tiles from the given sequence in the grid. When tile is placed, each cell which is located in fully occupied row or column is deleted (cells are deleted at the same time independently). You can place tile in the grid at any position, the only condition is that tiles (and tile parts) should not overlap. Your goal is to proceed all given figures and avoid crossing at any time.

The only line contains a string $$$s$$$ consisting of zeroes and ones ($$$1 \le |s| \le 1000$$$). Zero describes vertical tile, one describes horizontal tile.

Output $$$|s|$$$ lines — for each tile you should output two positive integers $$$r,c$$$, not exceeding $$$4$$$, representing numbers of smallest row and column intersecting with it. If there exist multiple solutions, print any of them.

NoteFollowing image illustrates the example after placing all three tiles:    Then the first row is deleted:


Today is tuesday, that means there is a dispute in JOHNNY SOLVING team again: they try to understand who is Johnny and who is Solving. That's why guys asked Umnik to help them. Umnik gave guys a connected graph with $$$n$$$ vertices without loops and multiedges, such that a degree of any vertex is at least $$$3$$$, and also he gave a number $$$1 \leq k \leq n$$$. Because Johnny is not too smart, he promised to find a simple path with length at least $$$\frac{n}{k}$$$ in the graph. In reply, Solving promised to find $$$k$$$ simple by vertices cycles with representatives, such that:   Length of each cycle is at least $$$3$$$.  Length of each cycle is not divisible by $$$3$$$.  In each cycle must be a representative - vertex, which belongs only to this cycle among all printed cycles. You need to help guys resolve the dispute, for that you need to find a solution for Johnny: a simple path with length at least $$$\frac{n}{k}$$$ ($$$n$$$ is not necessarily divided by $$$k$$$), or solution for Solving: $$$k$$$ cycles that satisfy all the conditions above. If there is no any solution - print $$$-1$$$.

The first line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \leq k \leq n \leq 2.5 \cdot 10^5, 1 \leq m \leq 5 \cdot 10^5$$$) Next $$$m$$$ lines describe edges of the graph in format $$$v$$$, $$$u$$$ ($$$1 \leq v, u \leq n$$$). It's guaranteed that $$$v \neq u$$$ and all $$$m$$$ pairs are distinct. It's guaranteed that a degree of each vertex is at least $$$3$$$.

Print PATH in the first line, if you solve problem for Johnny. In the second line print the number of vertices in the path $$$c$$$ ($$$c \geq \frac{n}{k}$$$). And in the third line print vertices describing the path in route order. Print CYCLES in the first line, if you solve problem for Solving. In the following lines describe exactly $$$k$$$ cycles in the following format: in the first line print the size of the cycle $$$c$$$ ($$$c \geq 3$$$). In the second line print the cycle in route order. Also, the first vertex in the cycle must be a representative. Print $$$-1$$$ if there is no any solution. The total amount of printed numbers in the output must be at most $$$10^6$$$. It's guaranteed, that if exists any solution then there is a correct output satisfies this restriction.


This is an interactive problem.Vasya and Petya are going to play the following game: Petya has some positive integer number $$$a$$$. After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers $$$(x, y)$$$. Petya will answer him:   "x", if $$$(x \bmod a) \geq (y \bmod a)$$$.  "y", if $$$(x \bmod a) < (y \bmod a)$$$. We define $$$(x \bmod a)$$$ as a remainder of division $$$x$$$ by $$$a$$$.Vasya should guess the number $$$a$$$ using no more, than 60 questions.It's guaranteed that Petya has a number, that satisfies the inequality $$$1 \leq a \leq 10^9$$$.Help Vasya playing this game and write a program, that will guess the number $$$a$$$.

NoteIn the first test, you should play $$$3$$$ games with Petya's numbers $$$1$$$, $$$2$$$ and $$$3$$$.In the first game, Petya will answer "x" (without quotes) to any question, because $$$(x \bmod 1) = 0$$$ for any integer $$$x$$$. In the second game, if you will ask pair $$$(0, 0)$$$, the answer will be "x" (without quotes), because $$$(0 \bmod 2) \geq (0 \bmod 2)$$$. But if you will ask pair $$$(2, 5)$$$, the answer will be "y" (without quotes), because $$$(2 \bmod 2) < (5 \bmod 2)$$$, because $$$(2 \bmod 2) = 0$$$ and $$$(5 \bmod 2) = 1$$$.


Vasya has his favourite number $$$n$$$. He wants to split it to some non-zero digits. It means, that he wants to choose some digits $$$d_1, d_2, \ldots, d_k$$$, such that $$$1 \leq d_i \leq 9$$$ for all $$$i$$$ and $$$d_1 + d_2 + \ldots + d_k = n$$$.Vasya likes beauty in everything, so he wants to find any solution with the minimal possible number of different digits among $$$d_1, d_2, \ldots, d_k$$$. Help him!

The first line contains a single integer $$$n$$$ — the number that Vasya wants to split ($$$1 \leq n \leq 1000$$$).

In the first line print one integer $$$k$$$ — the number of digits in the partition. Note that $$$k$$$ must satisfy the inequality $$$1 \leq k \leq n$$$. In the next line print $$$k$$$ digits $$$d_1, d_2, \ldots, d_k$$$ separated by spaces. All digits must satisfy the inequalities $$$1 \leq d_i \leq 9$$$. You should find a partition of $$$n$$$ in which the number of different digits among $$$d_1, d_2, \ldots, d_k$$$ will be minimal possible among all partitions of $$$n$$$ into non-zero digits. Among such partitions, it is allowed to find any. It is guaranteed that there exists at least one partition of the number $$$n$$$ into digits.

NoteIn the first test, the number $$$1$$$ can be divided into $$$1$$$ digit equal to $$$1$$$.In the second test, there are $$$3$$$ partitions of the number $$$4$$$ into digits in which the number of different digits is $$$1$$$. This partitions are $$$[1, 1, 1, 1]$$$, $$$[2, 2]$$$ and $$$[4]$$$. Any of these partitions can be found. And, for example, dividing the number $$$4$$$ to the digits $$$[1, 1, 2]$$$ isn't an answer, because it has $$$2$$$ different digits, that isn't the minimum possible number.


Two people are playing a game with a string $$$s$$$, consisting of lowercase latin letters. On a player's turn, he should choose two consecutive equal letters in the string and delete them. For example, if the string is equal to "xaax" than there is only one possible turn: delete "aa", so the string will become "xx". A player not able to make a turn loses.Your task is to determine which player will win if both play optimally.

The only line contains the string $$$s$$$, consisting of lowercase latin letters ($$$1 \leq |s| \leq 100\,000$$$), where $$$|s|$$$ means the length of a string $$$s$$$.

If the first player wins, print "Yes". If the second player wins, print "No".

NoteIn the first example the first player is unable to make a turn, so he loses.In the second example first player turns the string into "q", then second player is unable to move, so he loses.


Salem gave you $$$n$$$ sticks with integer positive lengths $$$a_1, a_2, \ldots, a_n$$$.For every stick, you can change its length to any other positive integer length (that is, either shrink or stretch it). The cost of changing the stick's length from $$$a$$$ to $$$b$$$ is $$$|a - b|$$$, where $$$|x|$$$ means the absolute value of $$$x$$$.A stick length $$$a_i$$$ is called almost good for some integer $$$t$$$ if $$$|a_i - t| \le 1$$$.Salem asks you to change the lengths of some sticks (possibly all or none), such that all sticks' lengths are almost good for some positive integer $$$t$$$ and the total cost of changing is minimum possible. The value of $$$t$$$ is not fixed in advance and you can choose it as any positive integer. As an answer, print the value of $$$t$$$ and the minimum cost. If there are multiple optimal choices for $$$t$$$, print any of them.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 1000$$$) — the number of sticks. The second line contains $$$n$$$ integers $$$a_i$$$ ($$$1 \le a_i \le 100$$$) — the lengths of the sticks.

Print the value of $$$t$$$ and the minimum possible cost. If there are multiple optimal choices for $$$t$$$, print any of them.

NoteIn the first example, we can change $$$1$$$ into $$$2$$$ and $$$10$$$ into $$$4$$$ with cost $$$|1 - 2| + |10 - 4| = 1 + 6 = 7$$$ and the resulting lengths $$$[2, 4, 4]$$$ are almost good for $$$t = 3$$$.In the second example, the sticks lengths are already almost good for $$$t = 2$$$, so we don't have to do anything.


Ayoub had an array $$$a$$$ of integers of size $$$n$$$ and this array had two interesting properties:   All the integers in the array were between $$$l$$$ and $$$r$$$ (inclusive).  The sum of all the elements was divisible by $$$3$$$. Unfortunately, Ayoub has lost his array, but he remembers the size of the array $$$n$$$ and the numbers $$$l$$$ and $$$r$$$, so he asked you to find the number of ways to restore the array. Since the answer could be very large, print it modulo $$$10^9 + 7$$$ (i.e. the remainder when dividing by $$$10^9 + 7$$$). In case there are no satisfying arrays (Ayoub has a wrong memory), print $$$0$$$.

The first and only line contains three integers $$$n$$$, $$$l$$$ and $$$r$$$ ($$$1 \le n \le 2 \cdot 10^5 , 1 \le l \le r \le 10^9$$$) — the size of the lost array and the range of numbers in the array.

Print the remainder when dividing by $$$10^9 + 7$$$ the number of ways to restore the array.

NoteIn the first example, the possible arrays are : $$$[1,2], [2,1], [3, 3]$$$.In the second example, the only possible array is $$$[2, 2, 2]$$$.


Given a string $$$s$$$ of length $$$n$$$ and integer $$$k$$$ ($$$1 \le k \le n$$$). The string $$$s$$$ has a level $$$x$$$, if $$$x$$$ is largest non-negative integer, such that it's possible to find in $$$s$$$:  $$$x$$$ non-intersecting (non-overlapping) substrings of length $$$k$$$,  all characters of these $$$x$$$ substrings are the same (i.e. each substring contains only one distinct character and this character is the same for all the substrings). A substring is a sequence of consecutive (adjacent) characters, it is defined by two integers $$$i$$$ and $$$j$$$ ($$$1 \le i \le j \le n$$$), denoted as $$$s[i \dots j]$$$ = "$$$s_{i}s_{i+1} \dots s_{j}$$$".For example, if $$$k = 2$$$, then:  the string "aabb" has level $$$1$$$ (you can select substring "aa"),  the strings "zzzz" and "zzbzz" has level $$$2$$$ (you can select two non-intersecting substrings "zz" in each of them),  the strings "abed" and "aca" have level $$$0$$$ (you can't find at least one substring of the length $$$k=2$$$ containing the only distinct character). Zuhair gave you the integer $$$k$$$ and the string $$$s$$$ of length $$$n$$$. You need to find $$$x$$$, the level of the string $$$s$$$.

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$) — the length of the string and the value of $$$k$$$. The second line contains the string $$$s$$$ of length $$$n$$$ consisting only of lowercase Latin letters.

Print a single integer $$$x$$$ — the level of the string.

NoteIn the first example, we can select $$$2$$$ non-intersecting substrings consisting of letter 'a': "(aa)ac(aa)bb", so the level is $$$2$$$.In the second example, we can select either substring "a" or "b" to get the answer $$$1$$$.


Kilani is playing a game with his friends. This game can be represented as a grid of size $$$n \times m$$$, where each cell is either empty or blocked, and every player has one or more castles in some cells (there are no two castles in one cell).The game is played in rounds. In each round players expand turn by turn: firstly, the first player expands, then the second player expands and so on. The expansion happens as follows: for each castle the player owns now, he tries to expand into the empty cells nearby. The player $$$i$$$ can expand from a cell with his castle to the empty cell if it's possible to reach it in at most $$$s_i$$$ (where $$$s_i$$$ is player's expansion speed) moves to the left, up, right or down without going through blocked cells or cells occupied by some other player's castle. The player examines the set of cells he can expand to and builds a castle in each of them at once. The turned is passed to the next player after that. The game ends when no player can make a move. You are given the game field and speed of the expansion for each player. Kilani wants to know for each player how many cells he will control (have a castle their) after the game ends.

The first line contains three integers $$$n$$$, $$$m$$$ and $$$p$$$ ($$$1 \le n, m \le 1000$$$, $$$1 \le p \le 9$$$) — the size of the grid and the number of players. The second line contains $$$p$$$ integers $$$s_i$$$ ($$$1 \le s \le 10^9$$$) — the speed of the expansion for every player. The following $$$n$$$ lines describe the game grid. Each of them consists of $$$m$$$ symbols, where '.' denotes an empty cell, '#' denotes a blocked cell and digit $$$x$$$ ($$$1 \le x \le p$$$) denotes the castle owned by player $$$x$$$. It is guaranteed, that each player has at least one castle on the grid.

Print $$$p$$$ integers — the number of cells controlled by each player after the game ends.

NoteThe picture below show the game before it started, the game after the first round and game after the second round in the first example:  In the second example, the first player is "blocked" so he will not capture new cells for the entire game. All other player will expand up during the first two rounds and in the third round only the second player will move to the left.


Hiasat registered a new account in NeckoForces and when his friends found out about that, each one of them asked to use his name as Hiasat's handle.Luckily for Hiasat, he can change his handle in some points in time. Also he knows the exact moments friends will visit his profile page. Formally, you are given a sequence of events of two types:  $$$1$$$ — Hiasat can change his handle.  $$$2$$$ $$$s$$$ — friend $$$s$$$ visits Hiasat's profile. The friend $$$s$$$ will be happy, if each time he visits Hiasat's profile his handle would be $$$s$$$.Hiasat asks you to help him, find the maximum possible number of happy friends he can get.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^5, 1 \le m \le 40$$$) — the number of events and the number of friends. Then $$$n$$$ lines follow, each denoting an event of one of two types:    $$$1$$$ — Hiasat can change his handle.  $$$2$$$ $$$s$$$ — friend $$$s$$$ ($$$1 \le |s| \le 40$$$) visits Hiasat's profile.  It's guaranteed, that each friend's name consists only of lowercase Latin letters. It's guaranteed, that the first event is always of the first type and each friend will visit Hiasat's profile at least once.

Print a single integer — the maximum number of happy friends.

NoteIn the first example, the best way is to change the handle to the "motarack" in the first event and to the "light" in the fourth event. This way, "motarack" and "light" will be happy, but "mike" will not.In the second example, you can choose either "alice", "bob" or "tanyaromanova" and only that friend will be happy.


Lunar New Year is approaching, and Bob decides to take a wander in a nearby park.The park can be represented as a connected graph with $$$n$$$ nodes and $$$m$$$ bidirectional edges. Initially Bob is at the node $$$1$$$ and he records $$$1$$$ on his notebook. He can wander from one node to another through those bidirectional edges. Whenever he visits a node not recorded on his notebook, he records it. After he visits all nodes at least once, he stops wandering, thus finally a permutation of nodes $$$a_1, a_2, \ldots, a_n$$$ is recorded.Wandering is a boring thing, but solving problems is fascinating. Bob wants to know the lexicographically smallest sequence of nodes he can record while wandering. Bob thinks this problem is trivial, and he wants you to solve it.A sequence $$$x$$$ is lexicographically smaller than a sequence $$$y$$$ if and only if one of the following holds:   $$$x$$$ is a prefix of $$$y$$$, but $$$x \ne y$$$ (this is impossible in this problem as all considered sequences have the same length);  in the first position where $$$x$$$ and $$$y$$$ differ, the sequence $$$x$$$ has a smaller element than the corresponding element in $$$y$$$.

The first line contains two positive integers $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 10^5$$$), denoting the number of nodes and edges, respectively. The following $$$m$$$ lines describe the bidirectional edges in the graph. The $$$i$$$-th of these lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \leq u_i, v_i \leq n$$$), representing the nodes the $$$i$$$-th edge connects. Note that the graph can have multiple edges connecting the same two nodes and self-loops. It is guaranteed that the graph is connected.

Output a line containing the lexicographically smallest sequence $$$a_1, a_2, \ldots, a_n$$$ Bob can record.

NoteIn the first sample, Bob's optimal wandering path could be $$$1 \rightarrow 2 \rightarrow 1 \rightarrow 3$$$. Therefore, Bob will obtain the sequence $$$\{1, 2, 3\}$$$, which is the lexicographically smallest one.In the second sample, Bob's optimal wandering path could be $$$1 \rightarrow 4 \rightarrow 3 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1 \rightarrow 5$$$. Therefore, Bob will obtain the sequence $$$\{1, 4, 3, 2, 5\}$$$, which is the lexicographically smallest one.


Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.There are $$$n$$$ positive integers $$$a_1, a_2, \ldots, a_n$$$ on Bob's homework paper, where $$$n$$$ is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least $$$2$$$ numbers. Suppose the numbers are divided into $$$m$$$ groups, and the sum of the numbers in the $$$j$$$-th group is $$$s_j$$$. Bob's aim is to minimize the sum of the square of $$$s_j$$$, that is $$$$$$\sum_{j = 1}^{m} s_j^2.$$$$$$Bob is puzzled by this hard problem. Could you please help him solve it?

The first line contains an even integer $$$n$$$ ($$$2 \leq n \leq 3 \cdot 10^5$$$), denoting that there are $$$n$$$ integers on Bob's homework paper. The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^4$$$), describing the numbers you need to deal with.

A single line containing one integer, denoting the minimum of the sum of the square of $$$s_j$$$, which is $$$$$$\sum_{i = j}^{m} s_j^2,$$$$$$ where $$$m$$$ is the number of groups.

NoteIn the first sample, one of the optimal solutions is to divide those $$$4$$$ numbers into $$$2$$$ groups $$$\{2, 8\}, \{5, 3\}$$$. Thus the answer is $$$(2 + 8)^2 + (5 + 3)^2 = 164$$$.In the second sample, one of the optimal solutions is to divide those $$$6$$$ numbers into $$$3$$$ groups $$$\{1, 2\}, \{1, 2\}, \{1, 2\}$$$. Thus the answer is $$$(1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27$$$.


Lunar New Year is approaching, and you bought a matrix with lots of "crosses".This matrix $$$M$$$ of size $$$n \times n$$$ contains only 'X' and '.' (without quotes). The element in the $$$i$$$-th row and the $$$j$$$-th column $$$(i, j)$$$ is defined as $$$M(i, j)$$$, where $$$1 \leq i, j \leq n$$$. We define a cross appearing in the $$$i$$$-th row and the $$$j$$$-th column ($$$1 < i, j < n$$$) if and only if $$$M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = $$$ 'X'.The following figure illustrates a cross appearing at position $$$(2, 2)$$$ in a $$$3 \times 3$$$ matrix. X.X.X.X.X Your task is to find out the number of crosses in the given matrix $$$M$$$. Two crosses are different if and only if they appear in different rows or columns.

The first line contains only one positive integer $$$n$$$ ($$$1 \leq n \leq 500$$$), denoting the size of the matrix $$$M$$$. The following $$$n$$$ lines illustrate the matrix $$$M$$$. Each line contains exactly $$$n$$$ characters, each of them is 'X' or '.'. The $$$j$$$-th element in the $$$i$$$-th line represents $$$M(i, j)$$$, where $$$1 \leq i, j \leq n$$$.

Output a single line containing only one integer number $$$k$$$ — the number of crosses in the given matrix $$$M$$$.

NoteIn the first sample, a cross appears at $$$(3, 3)$$$, so the answer is $$$1$$$.In the second sample, no crosses appear since $$$n < 3$$$, so the answer is $$$0$$$.In the third sample, crosses appear at $$$(3, 2)$$$, $$$(3, 4)$$$, $$$(4, 3)$$$, $$$(4, 5)$$$, so the answer is $$$4$$$.


Lunar New Year is approaching, and Bob is planning to go for a famous restaurant — "Alice's".The restaurant "Alice's" serves $$$n$$$ kinds of food. The cost for the $$$i$$$-th kind is always $$$c_i$$$. Initially, the restaurant has enough ingredients for serving exactly $$$a_i$$$ dishes of the $$$i$$$-th kind. In the New Year's Eve, $$$m$$$ customers will visit Alice's one after another and the $$$j$$$-th customer will order $$$d_j$$$ dishes of the $$$t_j$$$-th kind of food. The $$$(i + 1)$$$-st customer will only come after the $$$i$$$-th customer is completely served.Suppose there are $$$r_i$$$ dishes of the $$$i$$$-th kind remaining (initially $$$r_i = a_i$$$). When a customer orders $$$1$$$ dish of the $$$i$$$-th kind, the following principles will be processed. If $$$r_i > 0$$$, the customer will be served exactly $$$1$$$ dish of the $$$i$$$-th kind. The cost for the dish is $$$c_i$$$. Meanwhile, $$$r_i$$$ will be reduced by $$$1$$$. Otherwise, the customer will be served $$$1$$$ dish of the cheapest available kind of food if there are any. If there are multiple cheapest kinds of food, the one with the smallest index among the cheapest will be served. The cost will be the cost for the dish served and the remain for the corresponding dish will be reduced by $$$1$$$. If there are no more dishes at all, the customer will leave angrily. Therefore, no matter how many dishes are served previously, the cost for the customer is $$$0$$$.If the customer doesn't leave after the $$$d_j$$$ dishes are served, the cost for the customer will be the sum of the cost for these $$$d_j$$$ dishes.Please determine the total cost for each of the $$$m$$$ customers.

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 10^5$$$), representing the number of different kinds of food and the number of customers, respectively. The second line contains $$$n$$$ positive integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^7$$$), where $$$a_i$$$ denotes the initial remain of the $$$i$$$-th kind of dishes. The third line contains $$$n$$$ positive integers $$$c_1, c_2, \ldots, c_n$$$ ($$$1 \leq c_i \leq 10^6$$$), where $$$c_i$$$ denotes the cost of one dish of the $$$i$$$-th kind. The following $$$m$$$ lines describe the orders of the $$$m$$$ customers respectively. The $$$j$$$-th line contains two positive integers $$$t_j$$$ and $$$d_j$$$ ($$$1 \leq t_j \leq n$$$, $$$1 \leq d_j \leq 10^7$$$), representing the kind of food and the number of dishes the $$$j$$$-th customer orders, respectively.

Print $$$m$$$ lines. In the $$$j$$$-th line print the cost for the $$$j$$$-th customer.

NoteIn the first sample, $$$5$$$ customers will be served as follows. Customer $$$1$$$ will be served $$$6$$$ dishes of the $$$2$$$-nd kind, $$$1$$$ dish of the $$$4$$$-th kind, and $$$1$$$ dish of the $$$6$$$-th kind. The cost is $$$6 \cdot 3 + 1 \cdot 2 + 1 \cdot 2 = 22$$$. The remain of the $$$8$$$ kinds of food will be $$$\{8, 0, 2, 0, 4, 4, 7, 5\}$$$. Customer $$$2$$$ will be served $$$4$$$ dishes of the $$$1$$$-st kind. The cost is $$$4 \cdot 6 = 24$$$. The remain will be $$$\{4, 0, 2, 0, 4, 4, 7, 5\}$$$. Customer $$$3$$$ will be served $$$4$$$ dishes of the $$$6$$$-th kind, $$$3$$$ dishes of the $$$8$$$-th kind. The cost is $$$4 \cdot 2 + 3 \cdot 2 = 14$$$. The remain will be $$$\{4, 0, 2, 0, 4, 0, 7, 2\}$$$. Customer $$$4$$$ will be served $$$2$$$ dishes of the $$$3$$$-rd kind, $$$2$$$ dishes of the $$$8$$$-th kind. The cost is $$$2 \cdot 3 + 2 \cdot 2 = 10$$$. The remain will be $$$\{4, 0, 0, 0, 4, 0, 7, 0\}$$$. Customer $$$5$$$ will be served $$$7$$$ dishes of the $$$7$$$-th kind, $$$3$$$ dishes of the $$$1$$$-st kind. The cost is $$$7 \cdot 3 + 3 \cdot 6 = 39$$$. The remain will be $$$\{1, 0, 0, 0, 4, 0, 0, 0\}$$$.In the second sample, each customer is served what they order except the last one, who leaves angrily without paying. For example, the second customer is served $$$6$$$ dishes of the second kind, so the cost is $$$66 \cdot 6 = 396$$$.In the third sample, some customers may not be served what they order. For example, the second customer is served $$$6$$$ dishes of the second kind, $$$6$$$ of the third and $$$1$$$ of the fourth, so the cost is $$$66 \cdot 6 + 666 \cdot 6 + 6666 \cdot 1 = 11058$$$.


Lunar New Year is approaching, and Bob received a gift from his friend recently — a recursive sequence! He loves this sequence very much and wants to play with it.Let $$$f_1, f_2, \ldots, f_i, \ldots$$$ be an infinite sequence of positive integers. Bob knows that for $$$i > k$$$, $$$f_i$$$ can be obtained by the following recursive equation:$$$$$$f_i = \left(f_{i - 1} ^ {b_1} \cdot f_{i - 2} ^ {b_2} \cdot \cdots \cdot f_{i - k} ^ {b_k}\right) \bmod p,$$$$$$which in short is$$$$$$f_i = \left(\prod_{j = 1}^{k} f_{i - j}^{b_j}\right) \bmod p,$$$$$$where $$$p = 998\,244\,353$$$ (a widely-used prime), $$$b_1, b_2, \ldots, b_k$$$ are known integer constants, and $$$x \bmod y$$$ denotes the remainder of $$$x$$$ divided by $$$y$$$.Bob lost the values of $$$f_1, f_2, \ldots, f_k$$$, which is extremely troublesome – these are the basis of the sequence! Luckily, Bob remembers the first $$$k - 1$$$ elements of the sequence: $$$f_1 = f_2 = \ldots = f_{k - 1} = 1$$$ and the $$$n$$$-th element: $$$f_n = m$$$. Please find any possible value of $$$f_k$$$. If no solution exists, just tell Bob that it is impossible to recover his favorite sequence, regardless of Bob's sadness.

The first line contains a positive integer $$$k$$$ ($$$1 \leq k \leq 100$$$), denoting the length of the sequence $$$b_1, b_2, \ldots, b_k$$$. The second line contains $$$k$$$ positive integers $$$b_1, b_2, \ldots, b_k$$$ ($$$1 \leq b_i < p$$$). The third line contains two positive integers $$$n$$$ and $$$m$$$ ($$$k < n \leq 10^9$$$, $$$1 \leq m < p$$$), which implies $$$f_n = m$$$.

Output a possible value of $$$f_k$$$, where $$$f_k$$$ is a positive integer satisfying $$$1 \leq f_k < p$$$. If there are multiple answers, print any of them. If no such $$$f_k$$$ makes $$$f_n = m$$$, output $$$-1$$$ instead. It is easy to show that if there are some possible values of $$$f_k$$$, there must be at least one satisfying $$$1 \leq f_k < p$$$.

NoteIn the first sample, we have $$$f_4 = f_3^2 \cdot f_2^3 \cdot f_1^5$$$. Therefore, applying $$$f_3 = 4$$$, we have $$$f_4 = 16$$$. Note that there can be multiple answers.In the third sample, applying $$$f_7 = 1$$$ makes $$$f_{23333} = 1$$$.In the fourth sample, no such $$$f_1$$$ makes $$$f_{88888} = 66666$$$. Therefore, we output $$$-1$$$ instead.


Lunar New Year is approaching, and Bob is going to receive some red envelopes with countless money! But collecting money from red envelopes is a time-consuming process itself.Let's describe this problem in a mathematical way. Consider a timeline from time $$$1$$$ to $$$n$$$. The $$$i$$$-th red envelope will be available from time $$$s_i$$$ to $$$t_i$$$, inclusive, and contain $$$w_i$$$ coins. If Bob chooses to collect the coins in the $$$i$$$-th red envelope, he can do it only in an integer point of time between $$$s_i$$$ and $$$t_i$$$, inclusive, and he can't collect any more envelopes until time $$$d_i$$$ (inclusive) after that. Here $$$s_i \leq t_i \leq d_i$$$ holds.Bob is a greedy man, he collects coins greedily — whenever he can collect coins at some integer time $$$x$$$, he collects the available red envelope with the maximum number of coins. If there are multiple envelopes with the same maximum number of coins, Bob would choose the one whose parameter $$$d$$$ is the largest. If there are still multiple choices, Bob will choose one from them randomly.However, Alice — his daughter — doesn't want her father to get too many coins. She could disturb Bob at no more than $$$m$$$ integer time moments. If Alice decides to disturb Bob at time $$$x$$$, he could not do anything at time $$$x$$$ and resumes his usual strategy at the time $$$x + 1$$$ (inclusive), which may lead to missing some red envelopes.Calculate the minimum number of coins Bob would get if Alice disturbs him optimally.

The first line contains three non-negative integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \leq n \leq 10^5$$$, $$$0 \leq m \leq 200$$$, $$$1 \leq k \leq 10^5$$$), denoting the length of the timeline, the number of times Alice can disturb Bob and the total number of red envelopes, respectively. The following $$$k$$$ lines describe those $$$k$$$ red envelopes. The $$$i$$$-th line contains four positive integers $$$s_i$$$, $$$t_i$$$, $$$d_i$$$ and $$$w_i$$$ ($$$1 \leq s_i \leq t_i \leq d_i \leq n$$$, $$$1 \leq w_i \leq 10^9$$$) — the time segment when the $$$i$$$-th envelope is available, the time moment Bob can continue collecting after collecting the $$$i$$$-th envelope, and the number of coins in this envelope, respectively.

Output one integer — the minimum number of coins Bob would get if Alice disturbs him optimally.

NoteIn the first sample, Alice has no chance to disturb Bob. Therefore Bob will collect the coins in the red envelopes at time $$$1$$$ and $$$5$$$, collecting $$$13$$$ coins in total.In the second sample, Alice should disturb Bob at time $$$1$$$. Therefore Bob skips the first envelope, collects the second one and can not do anything after that. So the answer is $$$2$$$.


Today at the lesson of mathematics, Petya learns about the digital root.The digital root of a non-negative integer is the single digit value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. Let's denote the digital root of $$$x$$$ as $$$S(x)$$$. Then $$$S(5)=5$$$, $$$S(38)=S(3+8=11)=S(1+1=2)=2$$$, $$$S(10)=S(1+0=1)=1$$$.As a homework Petya got $$$n$$$ tasks of the form: find $$$k$$$-th positive number whose digital root is $$$x$$$.Petya has already solved all the problems, but he doesn't know if it's right. Your task is to solve all $$$n$$$ tasks from Petya's homework.

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^3$$$) — the number of tasks in Petya's homework. The next $$$n$$$ lines contain two integers $$$k_i$$$ ($$$1 \le k_i \le 10^{12}$$$) and $$$x_i$$$ ($$$1 \le x_i \le 9$$$) — $$$i$$$-th Petya's task in which you need to find a $$$k_i$$$-th positive number, the digital root of which is $$$x_i$$$.

Output $$$n$$$ lines, $$$i$$$-th line should contain a single integer — the answer to the $$$i$$$-th problem.


You are given a sequence $$$s$$$ consisting of $$$n$$$ digits from $$$1$$$ to $$$9$$$.You have to divide it into at least two segments (segment — is a consecutive sequence of elements) (in other words, you have to place separators between some digits of the sequence) in such a way that each element belongs to exactly one segment and if the resulting division will be represented as an integer numbers sequence then each next element of this sequence will be strictly greater than the previous one.More formally: if the resulting division of the sequence is $$$t_1, t_2, \dots, t_k$$$, where $$$k$$$ is the number of element in a division, then for each $$$i$$$ from $$$1$$$ to $$$k-1$$$ the condition $$$t_{i} < t_{i + 1}$$$ (using numerical comparing, it means that the integer representations of strings are compared) should be satisfied.For example, if $$$s=654$$$ then you can divide it into parts $$$[6, 54]$$$ and it will be suitable division. But if you will divide it into parts $$$[65, 4]$$$ then it will be bad division because $$$65 > 4$$$. If $$$s=123$$$ then you can divide it into parts $$$[1, 23]$$$, $$$[1, 2, 3]$$$ but not into parts $$$[12, 3]$$$.Your task is to find any suitable division for each of the $$$q$$$ independent queries.

The first line of the input contains one integer $$$q$$$ ($$$1 \le q \le 300$$$) — the number of queries. The first line of the $$$i$$$-th query contains one integer number $$$n_i$$$ ($$$2 \le n_i \le 300$$$) — the number of digits in the $$$i$$$-th query. The second line of the $$$i$$$-th query contains one string $$$s_i$$$ of length $$$n_i$$$ consisting only of digits from $$$1$$$ to $$$9$$$.

If the sequence of digits in the $$$i$$$-th query cannot be divided into at least two parts in a way described in the problem statement, print the single line "NO" for this query. Otherwise in the first line of the answer to this query print "YES", on the second line print $$$k_i$$$ — the number of parts in your division of the $$$i$$$-th query sequence and in the third line print $$$k_i$$$ strings $$$t_{i, 1}, t_{i, 2}, \dots, t_{i, k_i}$$$ — your division. Parts should be printed in order of the initial string digits. It means that if you write the parts one after another without changing their order then you'll get the string $$$s_i$$$. See examples for better understanding.


You are playing a new famous fighting game: Kortal Mombat XII. You have to perform a brutality on your opponent's character.You are playing the game on the new generation console so your gamepad have $$$26$$$ buttons. Each button has a single lowercase Latin letter from 'a' to 'z' written on it. All the letters on buttons are pairwise distinct.You are given a sequence of hits, the $$$i$$$-th hit deals $$$a_i$$$ units of damage to the opponent's character. To perform the $$$i$$$-th hit you have to press the button $$$s_i$$$ on your gamepad. Hits are numbered from $$$1$$$ to $$$n$$$.You know that if you press some button more than $$$k$$$ times in a row then it'll break. You cherish your gamepad and don't want to break any of its buttons.To perform a brutality you have to land some of the hits of the given sequence. You are allowed to skip any of them, however changing the initial order of the sequence is prohibited. The total damage dealt is the sum of $$$a_i$$$ over all $$$i$$$ for the hits which weren't skipped.Note that if you skip the hit then the counter of consecutive presses the button won't reset.Your task is to skip some hits to deal the maximum possible total damage to the opponent's character and not break your gamepad buttons.

The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$) — the number of hits and the maximum number of times you can push the same button in a row. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$), where $$$a_i$$$ is the damage of the $$$i$$$-th hit. The third line of the input contains the string $$$s$$$ consisting of exactly $$$n$$$ lowercase Latin letters — the sequence of hits (each character is the letter on the button you need to press to perform the corresponding hit).

Print one integer $$$dmg$$$ — the maximum possible damage to the opponent's character you can deal without breaking your gamepad buttons.

NoteIn the first example you can choose hits with numbers $$$[1, 3, 4, 5, 6, 7]$$$ with the total damage $$$1 + 16 + 18 + 7 + 2 + 10 = 54$$$.In the second example you can choose all hits so the total damage is $$$2 + 4 + 1 + 3 + 1000 = 1010$$$.In the third example you can choose all hits expect the third one so the total damage is $$$2 + 4 + 3 + 1000 = 1009$$$.In the fourth example you can choose hits with numbers $$$[2, 3, 6, 8]$$$. Only this way you can reach the maximum total damage $$$15 + 2 + 8 + 16 = 41$$$.In the fifth example you can choose only hits with numbers $$$[2, 4, 6]$$$ with the total damage $$$18 + 19 + 15 = 52$$$.In the sixth example you can change either first hit or the second hit (it does not matter) with the total damage $$$10$$$.


Vasya has a string $$$s$$$ of length $$$n$$$ consisting only of digits 0 and 1. Also he has an array $$$a$$$ of length $$$n$$$. Vasya performs the following operation until the string becomes empty: choose some consecutive substring of equal characters, erase it from the string and glue together the remaining parts (any of them can be empty). For example, if he erases substring 111 from string 111110 he will get the string 110. Vasya gets $$$a_x$$$ points for erasing substring of length $$$x$$$.Vasya wants to maximize his total points, so help him with this!

The first line contains one integer $$$n$$$ ($$$1 \le n \le 100$$$) — the length of string $$$s$$$. The second line contains string $$$s$$$, consisting only of digits 0 and 1. The third line contains $$$n$$$ integers $$$a_1, a_2, \dots a_n$$$ ($$$1 \le a_i \le 10^9$$$), where $$$a_i$$$ is the number of points for erasing the substring of length $$$i$$$.

Print one integer — the maximum total points Vasya can get.

NoteIn the first example the optimal sequence of erasings is: 1101001 $$$\rightarrow$$$ 111001 $$$\rightarrow$$$ 11101 $$$\rightarrow$$$ 1111 $$$\rightarrow$$$ $$$\varnothing$$$.In the second example the optimal sequence of erasings is: 10101 $$$\rightarrow$$$ 1001 $$$\rightarrow$$$ 11 $$$\rightarrow$$$ $$$\varnothing$$$.


Vasya wants to buy himself a nice new car. Unfortunately, he lacks some money. Currently he has exactly 0 burles.However, the local bank has $$$n$$$ credit offers. Each offer can be described with three numbers $$$a_i$$$, $$$b_i$$$ and $$$k_i$$$. Offers are numbered from $$$1$$$ to $$$n$$$. If Vasya takes the $$$i$$$-th offer, then the bank gives him $$$a_i$$$ burles at the beginning of the month and then Vasya pays bank $$$b_i$$$ burles at the end of each month for the next $$$k_i$$$ months (including the month he activated the offer). Vasya can take the offers any order he wants.Each month Vasya can take no more than one credit offer. Also each credit offer can not be used more than once. Several credits can be active at the same time. It implies that Vasya pays bank the sum of $$$b_i$$$ over all the $$$i$$$ of active credits at the end of each month.Vasya wants to buy a car in the middle of some month. He just takes all the money he currently has and buys the car of that exact price.Vasya don't really care what he'll have to pay the bank back after he buys a car. He just goes out of the country on his car so that the bank can't find him anymore.What is the maximum price that car can have?

The first line contains one integer $$$n$$$ ($$$1 \le n \le 500$$$) — the number of credit offers. Each of the next $$$n$$$ lines contains three integers $$$a_i$$$, $$$b_i$$$ and $$$k_i$$$ ($$$1 \le a_i, b_i, k_i \le 10^9$$$).

Print one integer — the maximum price of the car.

NoteIn the first example, the following sequence of offers taken is optimal: 4 $$$\rightarrow$$$ 3.The amount of burles Vasya has changes the following way: 5 $$$\rightarrow$$$ 32 $$$\rightarrow$$$ -86 $$$\rightarrow$$$ .... He takes the money he has in the middle of the second month (32 burles) and buys the car.The negative amount of money means that Vasya has to pay the bank that amount of burles.In the second example, the following sequence of offers taken is optimal: 3 $$$\rightarrow$$$ 1 $$$\rightarrow$$$ 2.The amount of burles Vasya has changes the following way: 0 $$$\rightarrow$$$ 300 $$$\rightarrow$$$ 338 $$$\rightarrow$$$ 1337 $$$\rightarrow$$$ 236 $$$\rightarrow$$$ -866 $$$\rightarrow$$$ ....


You are given a binary matrix $$$A$$$ of size $$$n \times n$$$. Let's denote an $$$x$$$-compression of the given matrix as a matrix $$$B$$$ of size $$$\frac{n}{x} \times \frac{n}{x}$$$ such that for every $$$i \in [1, n], j \in [1, n]$$$ the condition $$$A[i][j] = B[\lceil \frac{i}{x} \rceil][\lceil \frac{j}{x} \rceil]$$$ is met.Obviously, $$$x$$$-compression is possible only if $$$x$$$ divides $$$n$$$, but this condition is not enough. For example, the following matrix of size $$$2 \times 2$$$ does not have any $$$2$$$-compression: $$$01$$$   $$$10$$$ For the given matrix $$$A$$$, find maximum $$$x$$$ such that an $$$x$$$-compression of this matrix is possible.Note that the input is given in compressed form. But even though it is compressed, you'd better use fast input.

The first line contains one number $$$n$$$ ($$$4 \le n \le 5200$$$) — the number of rows and columns in the matrix $$$A$$$. It is guaranteed that $$$n$$$ is divisible by $$$4$$$. Then the representation of matrix follows. Each of $$$n$$$ next lines contains $$$\frac{n}{4}$$$ one-digit hexadecimal numbers (that is, these numbers can be represented either as digits from $$$0$$$ to $$$9$$$ or as uppercase Latin letters from $$$A$$$ to $$$F$$$). Binary representation of each of these numbers denotes next $$$4$$$ elements of the matrix in the corresponding row. For example, if the number $$$B$$$ is given, then the corresponding elements are 1011, and if the number is $$$5$$$, then the corresponding elements are 0101. Elements are not separated by whitespaces.

Print one number: maximum $$$x$$$ such that an $$$x$$$-compression of the given matrix is possible.


You have a garland consisting of $$$n$$$ lamps. Each lamp is colored red, green or blue. The color of the $$$i$$$-th lamp is $$$s_i$$$ ('R', 'G' and 'B' — colors of lamps in the garland).You have to recolor some lamps in this garland (recoloring a lamp means changing its initial color to another) in such a way that the obtained garland is nice.A garland is called nice if any two lamps of the same color have distance divisible by three between them. I.e. if the obtained garland is $$$t$$$, then for each $$$i, j$$$ such that $$$t_i = t_j$$$ should be satisfied $$$|i-j|~ mod~ 3 = 0$$$. The value $$$|x|$$$ means absolute value of $$$x$$$, the operation $$$x~ mod~ y$$$ means remainder of $$$x$$$ when divided by $$$y$$$.For example, the following garlands are nice: "RGBRGBRG", "GB", "R", "GRBGRBG", "BRGBRGB". The following garlands are not nice: "RR", "RGBG".Among all ways to recolor the initial garland to make it nice you have to choose one with the minimum number of recolored lamps. If there are multiple optimal solutions, print any of them.

The first line of the input contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of lamps. The second line of the input contains the string $$$s$$$ consisting of $$$n$$$ characters 'R', 'G' and 'B' — colors of lamps in the garland.

In the first line of the output print one integer $$$r$$$ — the minimum number of recolors needed to obtain a nice garland from the given one. In the second line of the output print one string $$$t$$$ of length $$$n$$$ — a nice garland obtained from the initial one with minimum number of recolors. If there are multiple optimal solutions, print any of them.


Recently you have received two positive integer numbers $$$x$$$ and $$$y$$$. You forgot them, but you remembered a shuffled list containing all divisors of $$$x$$$ (including $$$1$$$ and $$$x$$$) and all divisors of $$$y$$$ (including $$$1$$$ and $$$y$$$). If $$$d$$$ is a divisor of both numbers $$$x$$$ and $$$y$$$ at the same time, there are two occurrences of $$$d$$$ in the list.For example, if $$$x=4$$$ and $$$y=6$$$ then the given list can be any permutation of the list $$$[1, 2, 4, 1, 2, 3, 6]$$$. Some of the possible lists are: $$$[1, 1, 2, 4, 6, 3, 2]$$$, $$$[4, 6, 1, 1, 2, 3, 2]$$$ or $$$[1, 6, 3, 2, 4, 1, 2]$$$.Your problem is to restore suitable positive integer numbers $$$x$$$ and $$$y$$$ that would yield the same list of divisors (possibly in different order).It is guaranteed that the answer exists, i.e. the given list of divisors corresponds to some positive integers $$$x$$$ and $$$y$$$.

The first line contains one integer $$$n$$$ ($$$2 \le n \le 128$$$) — the number of divisors of $$$x$$$ and $$$y$$$. The second line of the input contains $$$n$$$ integers $$$d_1, d_2, \dots, d_n$$$ ($$$1 \le d_i \le 10^4$$$), where $$$d_i$$$ is either divisor of $$$x$$$ or divisor of $$$y$$$. If a number is divisor of both numbers $$$x$$$ and $$$y$$$ then there are two copies of this number in the list.

Print two positive integer numbers $$$x$$$ and $$$y$$$ — such numbers that merged list of their divisors is the permutation of the given list of integers. It is guaranteed that the answer exists.


Vasya got really tired of these credits (from problem F) and now wants to earn the money himself! He decided to make a contest to gain a profit.Vasya has $$$n$$$ problems to choose from. They are numbered from $$$1$$$ to $$$n$$$. The difficulty of the $$$i$$$-th problem is $$$d_i$$$. Moreover, the problems are given in the increasing order by their difficulties. The difficulties of all tasks are pairwise distinct. In order to add the $$$i$$$-th problem to the contest you need to pay $$$c_i$$$ burles to its author. For each problem in the contest Vasya gets $$$a$$$ burles.In order to create a contest he needs to choose a consecutive subsegment of tasks.So the total earnings for the contest are calculated as follows:   if Vasya takes problem $$$i$$$ to the contest, he needs to pay $$$c_i$$$ to its author;  for each problem in the contest Vasya gets $$$a$$$ burles;  let $$$gap(l, r) = \max\limits_{l \le i < r} (d_{i + 1} - d_i)^2$$$. If Vasya takes all the tasks with indices from $$$l$$$ to $$$r$$$ to the contest, he also needs to pay $$$gap(l, r)$$$. If $$$l = r$$$ then $$$gap(l, r) = 0$$$. Calculate the maximum profit that Vasya can earn by taking a consecutive segment of tasks.

The first line contains two integers $$$n$$$ and $$$a$$$ ($$$1 \le n \le 3 \cdot 10^5$$$, $$$1 \le a \le 10^9$$$) — the number of proposed tasks and the profit for a single problem, respectively. Each of the next $$$n$$$ lines contains two integers $$$d_i$$$ and $$$c_i$$$ ($$$1 \le d_i, c_i \le 10^9, d_i < d_{i+1}$$$).

Print one integer — maximum amount of burles Vasya can earn.


The only difference between easy and hard versions is a number of elements in the array.You are given an array $$$a$$$ consisting of $$$n$$$ integers. The value of the $$$i$$$-th element of the array is $$$a_i$$$.You are also given a set of $$$m$$$ segments. The $$$j$$$-th segment is $$$[l_j; r_j]$$$, where $$$1 \le l_j \le r_j \le n$$$.You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array $$$a = [0, 0, 0, 0, 0]$$$ and the given segments are $$$[1; 3]$$$ and $$$[2; 4]$$$ then you can choose both of them and the array will become $$$b = [-1, -2, -2, -1, 0]$$$.You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array $$$a$$$ and obtain the array $$$b$$$ then the value $$$\max\limits_{i=1}^{n}b_i - \min\limits_{i=1}^{n}b_i$$$ will be maximum possible.Note that you can choose the empty set.If there are multiple answers, you can print any.If you are Python programmer, consider using PyPy instead of Python when you submit your code.

The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 300, 0 \le m \le 300$$$) — the length of the array $$$a$$$ and the number of segments, respectively. The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^6 \le a_i \le 10^6$$$), where $$$a_i$$$ is the value of the $$$i$$$-th element of the array $$$a$$$. The next $$$m$$$ lines are contain two integers each. The $$$j$$$-th of them contains two integers $$$l_j$$$ and $$$r_j$$$ ($$$1 \le l_j \le r_j \le n$$$), where $$$l_j$$$ and $$$r_j$$$ are the ends of the $$$j$$$-th segment.

In the first line of the output print one integer $$$d$$$ — the maximum possible value $$$\max\limits_{i=1}^{n}b_i - \min\limits_{i=1}^{n}b_i$$$ if $$$b$$$ is the array obtained by applying some subset of the given segments to the array $$$a$$$. In the second line of the output print one integer $$$q$$$ ($$$0 \le q \le m$$$) — the number of segments you apply. In the third line print $$$q$$$ distinct integers $$$c_1, c_2, \dots, c_q$$$ in any order ($$$1 \le c_k \le m$$$) — indices of segments you apply to the array $$$a$$$ in such a way that the value $$$\max\limits_{i=1}^{n}b_i - \min\limits_{i=1}^{n}b_i$$$ of the obtained array $$$b$$$ is maximum possible. If there are multiple answers, you can print any.

NoteIn the first example the obtained array $$$b$$$ will be $$$[0, -4, 1, 1, 2]$$$ so the answer is $$$6$$$.In the second example the obtained array $$$b$$$ will be $$$[2, -3, 1, -1, 4]$$$ so the answer is $$$7$$$.In the third example you cannot do anything so the answer is $$$0$$$.


You have a garland consisting of $$$n$$$ lamps. Each lamp is colored red, green or blue. The color of the $$$i$$$-th lamp is $$$s_i$$$ ('R', 'G' and 'B' — colors of lamps in the garland).You have to recolor some lamps in this garland (recoloring a lamp means changing its initial color to another) in such a way that the obtained garland is diverse.A garland is called diverse if any two adjacent (consecutive) lamps (i. e. such lamps that the distance between their positions is $$$1$$$) have distinct colors.In other words, if the obtained garland is $$$t$$$ then for each $$$i$$$ from $$$1$$$ to $$$n-1$$$ the condition $$$t_i \ne t_{i + 1}$$$ should be satisfied.Among all ways to recolor the initial garland to make it diverse you have to choose one with the minimum number of recolored lamps. If there are multiple optimal solutions, print any of them.

In the first line of the output print one integer $$$r$$$ — the minimum number of recolors needed to obtain a diverse garland from the given one. In the second line of the output print one string $$$t$$$ of length $$$n$$$ — a diverse garland obtained from the initial one with minimum number of recolors. If there are multiple optimal solutions, print any of them.


Sasha likes programming. Once, during a very long contest, Sasha decided that he was a bit tired and needed to relax. So he did. But since Sasha isn't an ordinary guy, he prefers to relax unusually. During leisure time Sasha likes to upsolve unsolved problems because upsolving is very useful.Therefore, Sasha decided to upsolve the following problem:You have an array $$$a$$$ with $$$n$$$ integers. You need to count the number of funny pairs $$$(l, r)$$$ $$$(l \leq r)$$$. To check if a pair $$$(l, r)$$$ is a funny pair, take $$$mid = \frac{l + r - 1}{2}$$$, then if $$$r - l + 1$$$ is an even number and $$$a_l \oplus a_{l+1} \oplus \ldots \oplus a_{mid} = a_{mid + 1} \oplus a_{mid + 2} \oplus \ldots \oplus a_r$$$, then the pair is funny. In other words, $$$\oplus$$$ of elements of the left half of the subarray from $$$l$$$ to $$$r$$$ should be equal to $$$\oplus$$$ of elements of the right half. Note that $$$\oplus$$$ denotes the bitwise XOR operation.It is time to continue solving the contest, so Sasha asked you to solve this task.

The first line contains one integer $$$n$$$ ($$$2 \le n \le 3 \cdot 10^5$$$) — the size of the array. The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i < 2^{20}$$$) — array itself.

Print one integer — the number of funny pairs. You should consider only pairs where $$$r - l + 1$$$ is even number.

NoteBe as cool as Sasha, upsolve problems!In the first example, the only funny pair is $$$(2, 5)$$$, as $$$2 \oplus 3 = 4 \oplus 5 = 1$$$.In the second example, funny pairs are $$$(2, 3)$$$, $$$(1, 4)$$$, and $$$(3, 6)$$$.In the third example, there are no funny pairs.


Reading books is one of Sasha's passions. Once while he was reading one book, he became acquainted with an unusual character. The character told about himself like that: "Many are my names in many countries. Mithrandir among the Elves, Tharkûn to the Dwarves, Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not."And at that moment Sasha thought, how would that character be called in the East? In the East all names are palindromes. A string is a palindrome if it reads the same backward as forward. For example, such strings as "kazak", "oo" and "r" are palindromes, but strings "abb" and "ij" are not. Sasha believed that the hero would be named after one of the gods of the East. As long as there couldn't be two equal names, so in the East people did the following: they wrote the original name as a string on a piece of paper, then cut the paper minimum number of times $$$k$$$, so they got $$$k+1$$$ pieces of paper with substrings of the initial string, and then unite those pieces together to get a new string. Pieces couldn't be turned over, they could be shuffled.In this way, it's possible to achive a string abcdefg from the string f|de|abc|g using $$$3$$$ cuts (by swapping papers with substrings f and abc). The string cbadefg can't be received using the same cuts.More formally, Sasha wants for the given palindrome $$$s$$$ find such minimum $$$k$$$, that you can cut this string into $$$k + 1$$$ parts, and then unite them in such a way that the final string will be a palindrome and it won't be equal to the initial string $$$s$$$. It there is no answer, then print "Impossible" (without quotes).

The first line contains one string $$$s$$$ ($$$1 \le |s| \le 5\,000$$$) — the initial name, which consists only of lowercase Latin letters. It is guaranteed that $$$s$$$ is a palindrome.

Print one integer $$$k$$$ — the minimum number of cuts needed to get a new name, or "Impossible" (without quotes).

NoteIn the first example, you can cut the string in those positions: no|l|on, and then unite them as follows on|l|no. It can be shown that there is no solution with one cut.In the second example, you can cut the string right in the middle, and swap peaces, so you get toot.In the third example, you can't make a string, that won't be equal to the initial one.In the fourth example, you can cut the suffix nik and add it to the beginning, so you get nikkinnikkin.


Fedya and Sasha are friends, that's why Sasha knows everything about Fedya.Fedya keeps his patience in an infinitely large bowl. But, unlike the bowl, Fedya's patience isn't infinite, that is why let $$$v$$$ be the number of liters of Fedya's patience, and, as soon as $$$v$$$ becomes equal to $$$0$$$, the bowl will burst immediately. There is one tap in the bowl which pumps $$$s$$$ liters of patience per second. Notice that $$$s$$$ can be negative, in that case, the tap pumps out the patience. Sasha can do different things, so he is able to change the tap's speed. All actions that Sasha does can be represented as $$$q$$$ queries. There are three types of queries:  "1 t s"  — add a new event, means that starting from the $$$t$$$-th second the tap's speed will be equal to $$$s$$$.  "2 t"  — delete the event which happens at the $$$t$$$-th second. It is guaranteed that such event exists.  "3 l r v" — Sasha wonders: if you take all the events for which $$$l \le t \le r$$$ and simulate changes of Fedya's patience from the very beginning of the $$$l$$$-th second till the very beginning of the $$$r$$$-th second inclusive (the initial volume of patience, at the beginning of the $$$l$$$-th second, equals to $$$v$$$ liters) then when will be the moment when the bowl will burst. If that does not happen, then the answer will be $$$-1$$$. Since Sasha does not want to check what will happen when Fedya's patience ends, and he has already come up with the queries, he is asking you to help him and find the answer for each query of the $$$3$$$-rd type.It is guaranteed that at any moment of time, there won't be two events which happen at the same second.

The first line contans one integer $$$q$$$ ($$$1 \le q \le 10^5$$$)  — the number of queries. Each of the next $$$q$$$ lines have one of the following formats:   1 t s ($$$1 \le t \le 10^9$$$, $$$-10^9 \le s \le 10^9$$$), means that a new event is added, which means that starting from the $$$t$$$-th second the tap's speed will be equal to $$$s$$$.  2 t ($$$1 \le t \le 10^9$$$), means that the event which happens at the $$$t$$$-th second must be deleted. Guaranteed that such exists.  3 l r v ($$$1 \le l \le r \le 10^9$$$, $$$0 \le v \le 10^9$$$), means that you should simulate the process from the very beginning of the $$$l$$$-th second till the very beginning of the $$$r$$$-th second inclusive, and to say when will the bowl burst.  It is guaranteed that $$$t$$$, $$$s$$$, $$$l$$$, $$$r$$$, $$$v$$$ in all the queries are integers. Also, it is guaranteed that there is at least one query of the $$$3$$$-rd type, and there won't be a query of the $$$1$$$-st type with such $$$t$$$, that there already exists an event which happens at that second $$$t$$$.

For each query of the $$$3$$$-rd type, print in a new line the moment when the bowl will burst or print $$$-1$$$ if it won't happen. Your answer will be considered correct if it's absolute or relative error does not exceed $$$10^{-6}$$$. Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is accepted if and only if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$$$.

NoteIn the first example all the queries of the $$$3$$$-rd type cover all the events, it's simulation is following:


Once, during a lesson, Sasha got bored and decided to talk with his friends. Suddenly, he saw Kefa. Since we can talk endlessly about Kefa, we won't even start doing that. The conversation turned to graphs. Kefa promised Sasha to tell him about one interesting fact from graph theory if Sasha helps Kefa to count the number of beautiful trees. In this task, a tree is a weighted connected graph, consisting of $$$n$$$ vertices and $$$n-1$$$ edges, and weights of edges are integers from $$$1$$$ to $$$m$$$. Kefa determines the beauty of a tree as follows: he finds in the tree his two favorite vertices — vertices with numbers $$$a$$$ and $$$b$$$, and counts the distance between them. The distance between two vertices $$$x$$$ and $$$y$$$ is the sum of weights of edges on the simple path from $$$x$$$ to $$$y$$$. If the distance between two vertices $$$a$$$ and $$$b$$$ is equal to $$$m$$$, then the tree is beautiful.Sasha likes graph theory, and even more, Sasha likes interesting facts, that's why he agreed to help Kefa. Luckily, Sasha is familiar with you the best programmer in Byteland. Help Sasha to count the number of beautiful trees for Kefa. Two trees are considered to be distinct if there is an edge that occurs in one of them and doesn't occur in the other one. Edge's weight matters.Kefa warned Sasha, that there can be too many beautiful trees, so it will be enough to count the number modulo $$$10^9 + 7$$$.

The first line contains four integers $$$n$$$, $$$m$$$, $$$a$$$, $$$b$$$ ($$$2 \le n \le 10^6$$$, $$$1 \le m \le 10^6$$$, $$$1 \le a, b \le n$$$, $$$a \neq b$$$) — the number of vertices in the tree, the maximum weight of an edge and two Kefa's favorite vertices.

Print one integer — the number of beautiful trees modulo $$$10^9+7$$$.

NoteThere are $$$5$$$ beautiful trees in the first example:In the second example the following trees are beautiful:


You are given two segments $$$[l_1; r_1]$$$ and $$$[l_2; r_2]$$$ on the $$$x$$$-axis. It is guaranteed that $$$l_1 < r_1$$$ and $$$l_2 < r_2$$$. Segments may intersect, overlap or even coincide with each other.    The example of two segments on the $$$x$$$-axis. Your problem is to find two integers $$$a$$$ and $$$b$$$ such that $$$l_1 \le a \le r_1$$$, $$$l_2 \le b \le r_2$$$ and $$$a \ne b$$$. In other words, you have to choose two distinct integer points in such a way that the first point belongs to the segment $$$[l_1; r_1]$$$ and the second one belongs to the segment $$$[l_2; r_2]$$$.It is guaranteed that the answer exists. If there are multiple answers, you can print any of them.You have to answer $$$q$$$ independent queries.

The first line of the input contains one integer $$$q$$$ ($$$1 \le q \le 500$$$) — the number of queries. Each of the next $$$q$$$ lines contains four integers $$$l_{1_i}, r_{1_i}, l_{2_i}$$$ and $$$r_{2_i}$$$ ($$$1 \le l_{1_i}, r_{1_i}, l_{2_i}, r_{2_i} \le 10^9, l_{1_i} < r_{1_i}, l_{2_i} < r_{2_i}$$$) — the ends of the segments in the $$$i$$$-th query.

Print $$$2q$$$ integers. For the $$$i$$$-th query print two integers $$$a_i$$$ and $$$b_i$$$ — such numbers that $$$l_{1_i} \le a_i \le r_{1_i}$$$, $$$l_{2_i} \le b_i \le r_{2_i}$$$ and $$$a_i \ne b_i$$$. Queries are numbered in order of the input. It is guaranteed that the answer exists. If there are multiple answers, you can print any.