Problem Statement

In a parallel universe, AtCoder holds AtCoder Big Contest, where 10^{16} problems are given at once.
The IDs of the problems are as follows, from the 1-st problem in order: A, B, ..., Z, AA, AB, ..., ZZ, AAA, ...

In other words, the IDs are given in the following order:

• the strings of length 1 consisting of uppercase English letters, in lexicographical order;
• the strings of length 2 consisting of uppercase English letters, in lexicographical order;
• the strings of length 3 consisting of uppercase English letters, in lexicographical order;
• ...

Given a string S that is an ID of a problem given in this contest, find the index of the problem. (See also Samples.)

Constraints

• S is a valid ID of a problem given in AtCoder Big Contest.

Sample Input 1

AB

Sample Output 1

28

The problem whose ID is AB is the 28-th problem of AtCoder Big Contest, so 28 should be printed.

Sample Input 2

C

Sample Output 2

3

The problem whose ID is C is the 3-rd problem of AtCoder Big Contest, so 3 should be printed.

Sample Input 3

BRUTMHYHIIZP

Sample Output 3

10000000000000000

The problem whose ID is BRUTMHYHIIZP is the 10^{16}-th (last) problem of AtCoder Big Contest, so 10^{16} should be printed as an integer.

Problem Statement

You are given a string S = S_1S_2\ldots S_N of length N consisting of lowercase English letters.

Additionally, you are given Q queries about the string S. For i = 1, 2, \ldots, Q, the i-th query is represented by two integers l_i, r_i and asks the following.

In the substring S_{l_i}S_{l_i+1}\ldots S_{r_i} of S, which ranges from the l_i-th to the r_i-th character, how many places are there where the same lowercase English letter occurs twice in a row? In other words, how many integers p satisfy l_i \leq p \leq r_i-1 and S_p = S_{p+1}?

Print the answer for each of the Q queries.

Constraints

• N and Q are integers.
• 1 \leq N, Q \leq 3 \times 10^5
• S is a string of length N consisting of lowercase English letters.
• l_i and r_i are integers.
• 1 \leq l_i \leq r_i \leq N

Sample Input 1

11 4
mississippi
3 9
4 10
4 6
7 7

Sample Output 1

2
2
0
0

The answers to the four queries are as follows.

• For the first query, S_3S_4\ldots S_9 = ssissip has two places where the same lowercase English letter occurs twice in a row: S_3S_4 = ss and S_6S_7 = ss.
• For the second query, S_4S_5\ldots S_{10} = sissipp has two places where the same lowercase English letter occurs twice in a row: S_6S_7 = ss and S_9S_{10} = pp.
• For the third query, S_4S_5S_6 = sis has zero places where the same lowercase English letter occurs twice in a row.
• For the fourth query, S_7 = s has zero places where the same lowercase English letter occurs twice in a row.

Sample Input 2

5 1
aaaaa
1 5

Sample Output 2

4

S_1S_2\ldots S_5 = aaaaa has four places where the same lowercase English letter occurs twice in a row: S_1S_2 = aa, S_2S_3 = aa, S_3S_4 = aa, and S_4S_5 = aa.

Problem Statement

You are given an N \times N grid. Let (i,j) denote the cell in the i-th row from the top and the j-th column from the left.
The states of the cells are given by N strings of length N, S_1, S_2, \dots, S_N, in the following format:

• If the j-th character of S_i is o, there is an o written in cell (i,j).
• If the j-th character of S_i is x, there is an x written in cell (i,j).

Find the number of triples of cells that satisfy all of the following conditions:

• The three cells in the triple are distinct.
• All three cells have an o written in them.
• Exactly two of the cells are in the same row.
• Exactly two of the cells are in the same column.

Here, two triples are considered different if and only if some cell is contained in exactly one of the triples.

Constraints

• N is an integer between 2 and 2000, inclusive.
• S_i is a string of length N consisting of o and x.

Sample Input 1

3
ooo
oxx
xxo

Sample Output 1

4

The following four triples satisfy the conditions:

• (1,1),(1,2),(2,1)
• (1,1),(1,3),(2,1)
• (1,1),(1,3),(3,3)
• (1,2),(1,3),(3,3)

Sample Input 2

4
oxxx
xoxx
xxox
xxxo

Sample Output 2

0

Sample Input 3

15
xooxxooooxxxoox
oxxoxoxxxoxoxxo
oxxoxoxxxoxoxxx
ooooxooooxxoxxx
oxxoxoxxxoxoxxx
oxxoxoxxxoxoxxo
oxxoxooooxxxoox
xxxxxxxxxxxxxxx
xooxxxooxxxooox
oxxoxoxxoxoxxxo
xxxoxxxxoxoxxoo
xooxxxooxxoxoxo
xxxoxxxxoxooxxo
oxxoxoxxoxoxxxo
xooxxxooxxxooox

Sample Output 3

2960

Problem Statement

There are N boxes numbered 0 to N-1. Initially, box i contains A_i balls.

Takahashi will perform the following operations for i=1,2,\ldots,M in order:

• Set a variable C to 0.
• Take out all the balls from box B_i and hold them in hand.
• While holding at least one ball in hand, repeat the following process:
  • Increase the value of C by 1.
  • Put one ball from hand into box (B_i+C) \bmod N.

Determine the number of balls in each box after completing all operations.

Constraints

• 1 \leq N \leq 2\times 10^5
• 1 \leq M \leq 2\times 10^5
• 0 \leq A_i \leq 10^9
• 0 \leq B_i < N
• All input values are integers.

Sample Input 1

5 3
1 2 3 4 5
2 4 0

Sample Output 1

0 4 2 7 2

The operations proceed as follows:

Sample Input 2

3 10
1000000000 1000000000 1000000000
0 1 0 1 0 1 0 1 0 1

Sample Output 2

104320141 45436840 2850243019

Sample Input 3

1 4
1
0 0 0 0

Sample Output 3

1

Problem Statement

Given is a string S. How many different strings can be obtained as a permutation of a non-empty, not necessarily contiguous subsequence of S?

Since the count can be enormous, print it modulo 998244353.

Constraints

• S is a string of length 1 and 5000 (inclusive) consisting of lowercase English letters.

Sample Input 1

aab

Sample Output 1

8

There are 8 different strings that can be obtained as a permutation of a subsequence of S: a, b, aa, ab, ba, aab, aba, baa.

Sample Input 2

aaa

Sample Output 2

3

Sample Input 3

abcdefghijklmnopqrstuvwxyz

Sample Output 3

149621752

Be sure to print the count modulo 998244353.