Problem Statement

You are given a string S of length N consisting of A, B, and C.
Find the position where ABC first appears as a (contiguous) substring in S. In other words, find the smallest integer n that satisfies all of the following conditions.

• 1 \leq n \leq N - 2.
• The string obtained by extracting the n-th through (n+2)-th characters of S is ABC.

If ABC does not appear in S, print -1.

Constraints

• 3 \leq N \leq 100
• S is a string of length N consisting of A, B, and C.

Sample Input 1

8
ABABCABC

Sample Output 1

3

ABC first appears in S at the 3-rd through 5-th characters of S. Therefore, the answer is 3.

Sample Input 2

3
ACB

Sample Output 2

-1

If ABC does not appear in S, print -1.

Sample Input 3

20
BBAAABBACAACABCBABAB

Sample Output 3

13

Problem Statement

There was an exam consisting of three problems worth 1, 2, and 4 points.

Takahashi, Aoki, and Snuke took this exam. Takahashi scored A points, and Aoki scored B points.

Snuke solved all of the problems solved by at least one of Takahashi and Aoki, and failed to solve any of the problems solved by neither of them.

Find Snuke's score.

It can be proved that Snuke's score is uniquely determined under the Constraints of this problem.

Constraints

• 0\leq A,B \leq 7
• A and B are integers.

Sample Input 1

1 2

Sample Output 1

3

Since Takahashi scored 1 point, we see that he solved only the 1-point problem and failed to solve the other two.
Similarly, since Aoki scored 2 points, we see that he solved only the 2-point problem and failed to solve the other two.

Therefore, Snuke must have solved the 1- and 2-point problems, but not the 4-point one, which Takahashi and Aoki both failed to solve, for a score of 3 points. Thus, 3 should be printed.

Sample Input 2

5 3

Sample Output 2

7

Since Takahashi scored 5 points, we see that he solved the 1- and 4-point problems but not the 2-point one.
Similarly, since Aoki scored 3 points, we see that he solved the 1- and 2-point problems but not the 4-point one.

Therefore, each of the three problems is solved by at least one of Takahashi and Aoki, so we see that Snuke solved all of the problems, for a score of 7 points. Thus, 7 should be printed.

Sample Input 3

0 0

Sample Output 3

0

Both Takahashi and Aoki solved none of the problems. Therefore, so did Snuke. Thus, 0 should be printed.

Problem Statement

You are given an integer sequence A=(A_1,A_2,\ldots,A_N) of length N and integers L and R such that L\leq R.

For each i=1,2,\ldots,N, find the integer X_i that satisfies both of the following conditions. Note that the integer to be found is always uniquely determined.

• L\leq X_i \leq R.
• For every integer Y such that L \leq Y \leq R, it holds that |X_i - A_i| \leq |Y - A_i|.

Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq L\leq R \leq 10^9
• 1\leq A_i\leq 10^9
• All input values are integers.

Sample Input 1

5 4 7
3 1 4 9 7

Sample Output 1

4 4 4 7 7

For i=1:

• |4-3|=1
• |5-3|=2
• |6-3|=3
• |7-3|=4

Thus, X_i = 4.

Sample Input 2

3 10 10
11 10 9

Sample Output 2

10 10 10

Problem Statement

N participants, numbered 1 to N, will participate in a contest with M problems, numbered 1 to M.

For an integer i between 1 and N and an integer j between 1 and M, participant i can solve problem j if the j-th character of S_i is o, and cannot solve it if that character is x.

The participants must be in pairs. Print the number of ways to form a pair of participants who can collectively solve all the M problems.

More formally, print the number of pairs (x,y) of integers satisfying 1\leq x < y\leq N such that for any integer j between 1 and M, at least one of participant x and participant y can solve problem j.

Constraints

• N is an integer between 2 and 30, inclusive.
• M is an integer between 1 and 30, inclusive.
• S_i is a string of length M consisting of o and x.

Sample Input 1

5 5
ooooo
oooxx
xxooo
oxoxo
xxxxx

Sample Output 1

5

The following five pairs satisfy the condition: participants 1 and 2, participants 1 and 3, participants 1 and 4, participants 1 and 5, and participants 2 and 3.

On the other hand, the pair of participants 2 and 4, for instance, does not satisfy the condition because they cannot solve problem 4.

Sample Input 2

3 2
ox
xo
xx

Sample Output 2

1

Sample Input 3

2 4
xxxx
oxox

Sample Output 3

0

Problem Statement

There is a grid with H horizontal rows and W vertical columns. For two integers i and j such that 1 \leq i \leq H and 1 \leq j \leq W, the square at the i-th row from the top and j-th column from the left (which we denote by (i, j)) has an integer A_{i, j} written on it.

Takahashi is currently at (1,1). From now on, he repeats moving to an adjacent square to the right of or below his current square until he reaches (H, W). When he makes a move, he is not allowed to go outside the grid.

Takahashi will be happy if the integers written on the squares he visits (including initial (1, 1) and final (H, W)) are distinct. Find the number of his possible paths that make him happy.

Constraints

• 2 \leq H, W \leq 10
• 1 \leq A_{i, j} \leq 10^9
• All values in the input are integers.

Sample Input 1

3 3
3 2 2
2 1 3
1 5 4

Sample Output 1

3

There are six possible paths:

• (1, 1) \rightarrow (1, 2) \rightarrow (1, 3) \rightarrow (2, 3) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 2, 3, 4, so he will not be happy.
• (1, 1) \rightarrow (1, 2) \rightarrow (2, 2) \rightarrow (2, 3) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 3, 4, so he will not be happy.
• (1, 1) \rightarrow (1, 2) \rightarrow (2, 2) \rightarrow (3, 2) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 5, 4, so he will be happy.
• (1, 1) \rightarrow (2, 1) \rightarrow (2, 2) \rightarrow (2, 3) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 3, 4, so he will not be happy.
• (1, 1) \rightarrow (2, 1) \rightarrow (2, 2) \rightarrow (3, 2) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 5, 4, so he will be happy.
• (1, 1) \rightarrow (2, 1) \rightarrow (3, 1) \rightarrow (3, 2) \rightarrow (3, 3): the integers written on the squares he visits are 3, 2, 1, 5, 4, so he will be happy.

Thus, the third, fifth, and sixth paths described above make him happy.

Sample Input 2

10 10
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Sample Output 2

48620

In this example, every possible path makes him happy.