Problem Statement

You are given a string S consisting of lowercase English letters. The length of S is between 3 and 100, inclusive.

All characters but one of S are the same.

Find x such that the x-th character of S differs from all other characters.

Constraints

• S is a string of length between 3 and 100, inclusive, consisting of two different lowercase English letters.
• All characters but one of S are the same.

Sample Input 1

yay

Sample Output 1

2

The second character of yay differs from the first and third characters.

Sample Input 2

egg

Sample Output 2

1

Sample Input 3

zzzzzwz

Sample Output 3

6

Problem Statement

Takahashi likes full moons.

Let today be day 1. The first day on or after today on which he can see a full moon is day M. After that, he can see a full moon every P days, that is, on day M+P, day M+2P, and so on.

Find the number of days between day 1 and day N, inclusive, on which he can see a full moon.

Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq M \leq P \leq 2\times 10^5
• All input values are integers.

Sample Input 1

13 3 5

Sample Output 1

3

He can see a full moon on day 3, 8, 13, 18, and so on.

From day 1 to 13, he can see a full moon on three days: day 3, 8, and 13.

Sample Input 2

5 6 6

Sample Output 2

0

There may be no days he can see a full moon.

Sample Input 3

200000 314 318

Sample Output 3

628

Problem Statement

You are given two strings S and T consisting of lowercase English letters. The lengths of S and T are N and M, respectively. (The constraints guarantee that N \leq M.)

S is said to be a prefix of T when the first N characters of T coincide S.
S is said to be a suffix of T when the last N characters of T coincide S.

If S is both a prefix and a suffix of T, print 0;
If S is a prefix of T but not a suffix, print 1;
If S is a suffix of T but not a prefix, print 2;
If S is neither a prefix nor a suffix of T, print 3.

Constraints

• 1 \leq N \leq M \leq 100
• S is a string of length N consisting of lowercase English letters.
• T is a string of length M consisting of lowercase English letters.

Sample Input 1

3 7
abc
abcdefg

Sample Output 1

1

S is a prefix of T but not a suffix, so you should print 1.

Sample Input 2

3 4
abc
aabc

Sample Output 2

2

S is a suffix of T but not a prefix.

Sample Input 3

3 3
abc
xyz

Sample Output 3

3

S is neither a prefix nor a suffix of T.

Sample Input 4

3 3
aaa
aaa

Sample Output 4

0

S and T may coincide, in which case S is both a prefix and a suffix of T.

Problem Statement

You are given a tree with N vertices and N-1 edges.
The vertices are numbered 1,2,\ldots,N. The i-th edge connects Vertex a_i and Vertex b_i.

Determine whether this tree is a star.

Here, a star is a tree where there is a vertex directly connected to all other vertices.

Notes

For the definition of a tree, see Tree (graph theory) - Wikipedia.

Constraints

• 3 \leq N \leq 10^5
• 1 \leq a_i \lt b_i \leq N
• The given graph is a tree.

Sample Input 1

5
1 4
2 4
3 4
4 5

Sample Output 1

Yes

The given graph is a star.

Sample Input 2

4
2 4
1 4
2 3

Sample Output 2

No

The given graph is not a star.

Sample Input 3

10
9 10
3 10
4 10
8 10
1 10
2 10
7 10
6 10
5 10

Sample Output 3

Yes

Problem Statement

Planning to place many PCs in his room, Takahashi has decided to write a code that finds how many PCs he can place in his room.

You are given H strings S_1,S_2,\ldots,S_H, each of length W, consisting of . and T.

Takahashi may perform the following operation any number of times (possibly zero):

• Choose integers satisfying 1\leq i \leq H and 1 \leq j \leq W-1 such that the j-th and (j+1)-th characters of S_i are both T. Replace the j-th character of S_i with P, and (j+1)-th with C.

He tries to maximize the number of times he performs the operation. Find possible resulting S_1,S_2,\ldots,S_H.

Constraints

• 1\leq H \leq 100
• 2\leq W \leq 100
• H and W are integers.
• S_i is a string of length W consisting of . and T.

Sample Input 1

2 3
TTT
T.T

Sample Output 1

PCT
T.T

He can perform the operation at most once.

For example, an operation with (i,j)=(1,1) makes S_1 PCT.

Sample Input 2

3 5
TTT..
.TTT.
TTTTT

Sample Output 2

PCT..
.PCT.
PCTPC

Problem Statement

We have a playlist with N songs numbered 1, \dots, N.
Song i lasts A_i seconds.

When the playlist is played, song 1, song 2, \ldots, and song N play in this order. When song N ends, the playlist repeats itself, starting from song 1 again. While a song is playing, the next song does not play; when a song ends, the next song starts immediately.

At exactly T seconds after the playlist starts playing, which song is playing? Also, how many seconds have passed since the start of that song?
There is no input where the playlist changes songs at exactly T seconds after it starts playing.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq T \leq 10^{18}
• 1 \leq A_i \leq 10^9
• The playlist does not change songs at exactly T seconds after it starts playing.
• All values in the input are integers.

Sample Input 1

3 600
180 240 120

Sample Output 1

1 60

When the playlist is played, the following happens. (Assume that it starts playing at time 0.)

• From time 0 to time 180, song 1 plays.
• From time 180 to time 420, song 2 plays.
• From time 420 to time 540, song 3 plays.
• From time 540 to time 720, song 1 plays.
• From time 720 to time 960, song 2 plays.
• \qquad\vdots

At time 600, song 1 is playing, and 60 seconds have passed since the start of that song.

Sample Input 2

3 281
94 94 94

Sample Output 2

3 93

Sample Input 3

10 5678912340
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

6 678912340

Problem Statement

You are given an integer N and strings R and C of length N consisting of A, B, and C. Solve the following problem.

There is a N \times N grid. All cells are initially empty.
You can write at most one character from A, B, and C in each cell. (You can also leave the cell empty.)

Determine if it is possible to satisfy all of the following conditions, and if it is possible, print one way to do so.

• Each row and each column contain exactly one A, one B, and one C.
• The leftmost character written in the i-th row matches the i-th character of R.
• The topmost character written in the i-th column matches the i-th character of C.

Constraints

• N is an integer between 3 and 5, inclusive.
• R and C are strings of length N consisting of A, B, and C.

Sample Input 1

5
ABCBC
ACAAB

Sample Output 1

Yes
AC..B
.BA.C
C.BA.
BA.C.
..CBA

The grid in the output example satisfies all the following conditions, so it will be treated as correct.

• Each row contains exactly one A, one B, and one C.
• Each column contains exactly one A, one B, and one C.
• The leftmost characters written in the rows are A, B, C, B, C from top to bottom.
• The topmost characters written in the columns are A, C, A, A, B from left to right.

Sample Input 2

3
AAA
BBB

Sample Output 2

No

For this input, there is no way to fill the grid to satisfy the conditions.

Problem Statement

You are given a sequence of N-1 integers S = (S_1, S_2, \ldots, S_{N-1}), and M distinct integers X_1, X_2, \ldots, X_M, which are called lucky numbers.

A sequence of N integers A = (A_1, A_2, \ldots, A_N) satisfying the following condition is called a good sequence.

A_i + A_{i+1} = S_i holds for every i = 1, 2, \ldots, N-1.

Find the maximum possible number of terms that are lucky numbers in a good sequence A, that is, the maximum possible number of integers i between 1 and N such that A_i \in \lbrace X_1, X_2, \ldots, X_M \rbrace.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq M \leq 10
• -10^9 \leq S_i \leq 10^9
• -10^9 \leq X_i \leq 10^9
• X_1 \lt X_2 \lt \cdots \lt X_M
• All values in input are integers.

Sample Input 1

9 2
2 3 3 4 -4 -7 -4 -1
-1 5

Sample Output 1

4

A good sequence A = (3, -1, 4, -1, 5, -9, 2, -6, 5) contains four terms that are lucky numbers: A_2, A_4, A_5, A_9, which is the maximum possible count.

Sample Input 2

20 10
-183260318 206417795 409343217 238245886 138964265 -415224774 -499400499 -313180261 283784093 498751662 668946791 965735441 382033304 177367159 31017484 27914238 757966050 878978971 73210901
-470019195 -379631053 -287722161 -231146414 -84796739 328710269 355719851 416979387 431167199 498905398

Sample Output 2

8

Problem Statement

There is a row of N squares labeled 1,2,\dots,N and a sequence A=(A_1,A_2,\dots,A_N) of length N.
Initially, square 1 is painted black, the other N-1 squares are painted white, and a piece is placed on square 1.

You may repeat the following operation any number of times, possibly zero:

• When the piece is on square i, choose a positive integer x and move the piece to square i + A_i \times x.
  • Here, you cannot make a move with i + A_i \times x > N.
• Then, paint the square i + A_i \times x black.

Find the number of possible sets of squares that can be painted black at the end of the operations, modulo 998244353.

Constraints

• All input values are integers.
• 1 \le N \le 2 \times 10^5
• 1 \le A_i \le 2 \times 10^5

Sample Input 1

5
1 2 3 1 1

Sample Output 1

8

There are eight possible sets of squares painted black:

• Square 1
• Squares 1,2
• Squares 1,2,4
• Squares 1,2,4,5
• Squares 1,3
• Squares 1,4
• Squares 1,4,5
• Squares 1,5

Sample Input 2

1
200000

Sample Output 2

1

Sample Input 3

40
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Output 3

721419738

Be sure to find the number modulo 998244353.