Problem Statement

Takahashi sent a string T consisting of lowercase English letters to Aoki. As a result, Aoki received a string T' consisting of lowercase English letters.

T' may have been altered from T. Specifically, exactly one of the following four conditions is known to hold.

• T' is equal to T.
• T' is a string obtained by inserting one lowercase English letter at one position (possibly the beginning and end) in T.
• T' is a string obtained by deleting one character from T.
• T' is a string obtained by changing one character in T to another lowercase English letter.

You are given the string T' received by Aoki and N strings S_1, S_2, \ldots, S_N consisting of lowercase English letters. Find all the strings among S_1, S_2, \ldots, S_N that could equal the string T sent by Takahashi.

Constraints

• N is an integer.
• 1 \leq N \leq 5 \times 10^5
• S_i and T' are strings of length between 1 and 5 \times 10^5, inclusive, consisting of lowercase English letters.
• The total length of S_1, S_2, \ldots, S_N is at most 5 \times 10^5.

Sample Input 1

5 ababc
ababc
babc
abacbc
abdbc
abbac

Sample Output 1

4
1 2 3 4

Among S_1, S_2, \ldots, S_5, the strings that could be equal to T are S_1, S_2, S_3, S_4, as explained below.

• S_1 could be equal to T, because T' = ababc is equal to S_1 = ababc.
• S_2 could be equal to T, because T' = ababc is obtained by inserting the letter a at the beginning of S_2 = babc.
• S_3 could be equal to T, because T' = ababc is obtained by deleting the fourth character c from S_3 = abacbc.
• S_4 could be equal to T, because T' = ababc is obtained by changing the third character d in S_4 = abdbc to b.
• S_5 could not be equal to T, because if we take S_5 = abbac as T, then T' = ababc does not satisfy any of the four conditions in the problem statement.

Sample Input 2

1 aoki
takahashi

Sample Output 2

0

Sample Input 3

9 atcoder
atoder
atcode
athqcoder
atcoder
tacoder
jttcoder
atoder
atceoder
atcoer

Sample Output 3

6
1 2 4 7 8 9

Problem Statement

Takahashi has a red jewel of level N. (He has no other jewels.)
Takahashi can do the following operations any number of times.

• Convert a red jewel of level n (n is at least 2) into "a red jewel of level (n-1) and X blue jewels of level n".
• Convert a blue jewel of level n (n is at least 2) into "a red jewel of level (n-1) and Y blue jewels of level (n-1)".

Takahashi wants as many blue jewels of level 1 as possible. At most, how many blue jewels of level 1 can he obtain by the operations?

Constraints

• 1 \leq N \leq 10
• 1 \leq X \leq 5
• 1 \leq Y \leq 5
• All values in input are integers.

Sample Input 1

2 3 4

Sample Output 1

12

Takahashi can obtain 12 blue jewels of level 1 by the following conversions.

• First, he converts a red jewel of level 2 into a red jewel of level 1 and 3 blue jewels of level 2.
  • After this operation, Takahashi has 1 red jewel of level 1 and 3 blue jewels of level 2.
• Next, he repeats the following conversion 3 times: converting a blue jewel of level 2 into a red jewel of level 1 and 4 blue jewels of level 1.
  • After these operations, Takahashi has 4 red jewels of level 1 and 12 blue jewels of level 1.
• He cannot perform a conversion anymore.

He cannot obtain more than 12 blue jewels of level 1, so the answer is 12.

Sample Input 2

1 5 5

Sample Output 2

0

Takahashi may not be able to obtain a blue jewel of level 1.

Sample Input 3

10 5 5

Sample Output 3

3942349900

Note that the answer may not fit into a 32-bit integer type.

Problem Statement

We have a long piece of timber with a length of L meters.
For each x = 1, 2, \dots, L - 1, there is a mark called Mark x at x meters from the left end of the piece.

You are given Q queries, the i-th of which is represented as a pair of numbers (c_i, x_i).
Process the queries in ascending order of i as described below.

• If c_i = 1: cut the piece at Mark x_i into two.
• If c_i = 2: choose the piece with Mark x_i on it and print its length.

Here, for both kinds of queries c_i = 1, 2, it is guaranteed that there will have been no cut at Mark x_i when the query is to be processed.

Constraints

• 1 \leq L \leq 10^9
• 1 \leq Q \leq 2 \times 10^5
• c_i = 1, 2 (1 \leq i \leq Q)
• 1 \leq x_i \leq L - 1 (1 \leq i \leq Q)
• For every i (1 \leq i \leq Q), the following holds: there is no j such that 1 \leq j \lt i and (c_j,x_j) = (1, x_i).
• All values in input are integers.

Sample Input 1

5 3
2 2
1 3
2 2

Sample Output 1

5
3

At the time of the first query, no cut has been made, so the piece with Mark 2 has a length of 5 meters. Thus, you should print 5.
In the second query, the piece is cut into two pieces with lengths of 3 and 2 meters.
At the time of the third query, the piece with Mark 2 has a length of 3 meters, so you should print 3.

Sample Input 2

5 3
1 2
1 4
2 3

Sample Output 2

2

Sample Input 3

100 10
1 31
2 41
1 59
2 26
1 53
2 58
1 97
2 93
1 23
2 84

Sample Output 3

69
31
6
38
38

Problem Statement

You are given a length-N sequence A=(A_1,A_2,\dots,A_N) consisting of 0, 1, and 2, and a length-N string S=S_1S_2\dots S_N consisting of M, E, and X.

Find the sum of \text{mex}(A_i,A_j,A_k) over all tuples of integers (i,j,k) such that 1 \leq i < j < k \leq N and S_iS_jS_k= MEX. Here, \text{mex}(A_i,A_j,A_k) denotes the minimum non-negative integer that equals neither A_i,A_j, nor A_k.

Constraints

• 3\leq N \leq 2\times 10^5
• N is an integer.
• A_i \in \lbrace 0,1,2\rbrace
• S is a string of length N consisting of M, E, and X.

Sample Input 1

4
1 1 0 2
MEEX

Sample Output 1

3

The tuples (i,j,k)\ (1 \leq i < j < k \leq N) such that S_iS_jS_k = MEX are the following two: (i,j,k)=(1,2,4),(1,3,4). Since \text{mex}(A_1,A_2,A_4)=\text{mex}(1,1,2)=0 and \text{mex}(A_1,A_3,A_4)=\text{mex}(1,0,2)=3, the answer is 0+3=3.

Sample Input 2

3
0 0 0
XXX

Sample Output 2

0

Sample Input 3

15
1 1 2 0 0 2 0 2 0 0 0 0 0 2 2
EXMMXXXEMEXEXMM

Sample Output 3

13