Problem Statement

A string S is said to be a substring of a string T when there is a pair of integers i and j (1 \leq i \leq j \leq |T|) that satisfy the following condition.

• The extraction of the i-th through j-th characters of T without changing the order equals S.

Let T be the concatenation of 10^5 copies of oxx.
Given a string S, print Yes if S is a substring of T, and No otherwise.

Constraints

• S is a string consisting of o and x.
• The length of S is between 1 and 10 (inclusive).

Sample Input 1

xoxxoxxo

Sample Output 1

Yes

T begins like this: oxxoxxoxxoxx... Since the extraction of 3-rd through 10-th characters of T equals S, S is a substring of T, so Yes should be printed.

Sample Input 2

xxoxxoxo

Sample Output 2

No

Since there is no way to extract from T a string that equals S, S is not a substring of T, so No should be printed.

Sample Input 3

ox

Sample Output 3

Yes

Problem Statement

There is a grid with H rows and W columns; initially, all cells are painted white. Let (i, j) denote the cell at the i-th row from the top and the j-th column from the left.

This grid is considered to be toroidal. That is, (i, 1) is to the right of (i, W) for each 1 \leq i \leq H, and (1, j) is below (H, j) for each 1 \leq j \leq W.

Takahashi is at (1, 1) and facing upwards. Print the color of each cell in the grid after Takahashi repeats the following operation N times.

• If the current cell is painted white, repaint it black, rotate 90^\circ clockwise, and move forward one cell in the direction he is facing. Otherwise, repaint the current cell white, rotate 90^\circ counterclockwise, and move forward one cell in the direction he is facing.

Constraints

• 1 \leq H, W \leq 100
• 1 \leq N \leq 1000
• All input values are integers.

Sample Input 1

3 4 5

Sample Output 1

.#..
##..
....

The cells of the grid change as follows due to the operations:

....   #...   ##..   ##..   ##..   .#..
.... → .... → .... → .#.. → ##.. → ##..
....   ....   ....   ....   ....   ....

Sample Input 2

2 2 1000

Sample Output 2

..
..

Sample Input 3

10 10 10

Sample Output 3

##........
##........
..........
..........
..........
..........
..........
..........
..........
#........#

Problem Statement

You are given an integer sequence A=(A_1,A_2,\dots,A_N) of length N.

Find the maximum value of \displaystyle \sum_{i=1}^{M} i \times B_i for a contiguous subarray B=(B_1,B_2,\dots,B_M) of A of length M.

Notes

A contiguous subarray of a number sequence is a sequence that is obtained by removing 0 or more initial terms and 0 or more final terms from the original number sequence.

For example, (2, 3) and (1, 2, 3) are contiguous subarrays of (1, 2, 3, 4), but (1, 3) and (3,2,1) are not contiguous subarrays of (1, 2, 3, 4).

Constraints

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

Sample Input 1

4 2
5 4 -1 8

Sample Output 1

15

When B=(A_3,A_4), we have \displaystyle \sum_{i=1}^{M} i \times B_i = 1 \times (-1) + 2 \times 8 = 15. Since it is impossible to achieve 16 or a larger value, the solution is 15.

Note that you are not allowed to choose, for instance, B=(A_1,A_4).

Sample Input 2

10 4
-3 1 -4 1 -5 9 -2 6 -5 3

Sample Output 2

31

Problem Statement

You are given a sequence A=(A_1,A_2,\dots,A_{3N}) of length 3N where each of 1,2,\dots, and N occurs exactly three times.

For i=1,2,\dots,N, let f(i) be the index of the middle occurrence of i in A. Sort 1,2,\dots,N in ascending order of f(i).

Formally, f(i) is defined as follows.

• Suppose that those j such that A_j = i are j=\alpha,\beta,\gamma\ (\alpha < \beta < \gamma). Then, f(i) = \beta.

Constraints

• 1\leq N \leq 10^5
• 1 \leq A_j \leq N
• i occurs in A exactly three times, for each i=1,2,\dots,N.
• All input values are integers.

Sample Input 1

3
1 1 3 2 3 2 2 3 1

Sample Output 1

1 3 2

• 1 occurs in A at A_1,A_2,A_9, so f(1) = 2.
• 2 occurs in A at A_4,A_6,A_7, so f(2) = 6.
• 3 occurs in A at A_3,A_5,A_8, so f(3) = 5.

Thus, f(1) < f(3) < f(2), so 1,3, and 2 should be printed in this order.

Sample Input 2

1
1 1 1

Sample Output 2

1

Sample Input 3

4
2 3 4 3 4 1 3 1 1 4 2 2

Sample Output 3

3 4 1 2

Problem Statement

A sequence of n numbers, S = (s_1, s_2, \dots, s_n), is said to be non-decreasing if and only if s_i \leq s_{i+1} holds for every i (1 \leq i \leq n - 1).

Given are non-decreasing sequences of N integers each: A = (a_1, a_2, \dots, a_N) and B = (b_1, b_2, \dots, b_N).
Consider a non-decreasing sequence of N integers, C = (c_1, c_2, \dots, c_N), that satisfies the following condition:

• a_i \leq c_i \leq b_i for every i (1 \leq i \leq N).

Find the number, modulo 998244353, of sequences that can be C.

Constraints

• 1 \leq N \leq 3000
• 0 \leq a_i \leq b_i \leq 3000 (1 \leq i \leq N)
• The sequences A and B are non-decreasing.
• All values in input are integers.

Sample Input 1

2
1 1
2 3

Sample Output 1

5

There are five sequences that can be C, as follows.

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

Note that (2, 1) does not satisfy the condition since it is not non-decreasing.

Sample Input 2

3
2 2 2
2 2 2

Sample Output 2

1

There is one sequence that can be C, as follows.

• (2, 2, 2)

Sample Input 3

10
1 2 3 4 5 6 7 8 9 10
1 4 9 16 25 36 49 64 81 100

Sample Output 3

978222082

Be sure to find the count modulo 998244353.