Problem Statement

The following five days are called the five seasonal festivals (gosekku).

• January \color{red}{\mathbf{7}}
• March 3
• May 5
• July 7
• September 9

If month M, day D is one of the five seasonal festivals, output Yes; otherwise, output No.

Constraints

• M and D are integers.
• Month M, day D is a valid date in a leap year in the Gregorian calendar.

Sample Input 1

3 3

Sample Output 1

Yes

March 3 is one of the five seasonal festivals, so output Yes.

Sample Input 2

1 1

Sample Output 2

No

January 1 is not one of the five seasonal festivals, so output No.

Sample Input 3

4 4

Sample Output 3

No

Sample Input 4

11 7

Sample Output 4

No

Problem Statement

You are given positive integers N and M.

If the following operation is repeated while the value of M is not 0, find the number of operations performed.

• Let x be the remainder when N is divided by M. Replace the value of M with x.

It can be proved that M becomes 0 after a finite number of operations.

Constraints

• 1 \leq N, M \leq 1000
• All input values are integers.

Sample Input 1

8 5

Sample Output 1

3

Initially, N = 8 and M = 5.

The remainder when 8 is divided by 5 is 3, so M = 3 after one operation.

The remainder when 8 is divided by 3 is 2, so M = 2 after two operations.

The remainder when 8 is divided by 2 is 0, so M = 0 after three operations.

Thus, output 3 as the answer.

Sample Input 2

14 6

Sample Output 2

2

Sample Input 3

460 33

Sample Output 3

5

Problem Statement

There are N people. The family name and given name of the i-th person (1 \leq i \leq N) are S_i and T_i, respectively.

Determine whether there is a pair of people with the same family and given names. In other words, determine whether there is a pair of integers (i,j) such that 1 \leq i \lt j \leq N, S_i=S_j, and T_i=T_j.

Constraints

• 2 \leq N \leq 1000
• N is an integer.
• Each of S_i and T_i is a string of length between 1 and 10 (inclusive) consisting of English lowercase letters.

Sample Input 1

3
tanaka taro
sato hanako
tanaka taro

Sample Output 1

Yes

The first and third persons have the same family and given names.

Sample Input 2

3
saito ichiro
saito jiro
saito saburo

Sample Output 2

No

No two persons have the same family and given names.

Sample Input 3

4
sypdgidop bkseq
bajsqz hh
ozjekw mcybmtt
qfeysvw dbo

Sample Output 3

No

Problem Statement

You are given N-by-N matrices A and B where each element is 0 or 1.
Let A_{i,j} and B_{i,j} denote the element at the i-th row and j-th column of A and B, respectively.
Determine whether it is possible to rotate A so that B_{i,j} = 1 for every pair of integers (i, j) such that A_{i,j} = 1.
Here, to rotate A is to perform the following operation zero or more times:

• for every pair of integers (i, j) such that 1 \leq i, j \leq N, simultaneously replace A_{i,j} with A_{N + 1 - j,i}.

Constraints

• 1 \leq N \leq 100
• Each element of A and B is 0 or 1.
• All values in the input are integers.

Sample Input 1

3
0 1 1
1 0 0
0 1 0
1 1 0
0 0 1
1 1 1

Sample Output 1

Yes

Initially, A is :

0 1 1
1 0 0
0 1 0

After performing the operation once, A is :

0 1 0
1 0 1 
0 0 1

After performing the operation once again, A is :

0 1 0
0 0 1
1 1 0

Here, B_{i,j} = 1 for every pair of integers (i, j) such that A_{i,j} = 1, so you should print Yes.

Sample Input 2

2
0 0
0 0
1 1
1 1

Sample Output 2

Yes

Sample Input 3

5
0 0 1 1 0
1 0 0 1 0
0 0 1 0 1
0 1 0 1 0
0 1 0 0 1
1 1 0 0 1
0 1 1 1 0
0 0 1 1 1
1 0 1 0 1
1 1 0 1 0

Sample Output 3

No

Problem Statement

There is an N\times N grid with horizontal rows and vertical columns, where all squares are initially painted white. Let (i,j) denote the square at the i-th row and j-th column.

Takahashi has integers A and B, which are between 1 and N (inclusive). He will do the following operations.

• For every integer k such that \max(1-A,1-B)\leq k\leq \min(N-A,N-B), paint (A+k,B+k) black.
• For every integer k such that \max(1-A,B-N)\leq k\leq \min(N-A,B-1), paint (A+k,B-k) black.

In the grid after these operations, find the color of each square (i,j) such that P\leq i\leq Q and R\leq j\leq S.

Constraints

• 1 \leq N \leq 10^{18}
• 1 \leq A \leq N
• 1 \leq B \leq N
• 1 \leq P \leq Q \leq N
• 1 \leq R \leq S \leq N
• (Q-P+1)\times(S-R+1)\leq 3\times 10^5
• All values in input are integers.

Sample Input 1

5 3 2
1 5 1 5

Sample Output 1

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

The first operation paints the four squares (2,1), (3,2), (4,3), (5,4) black, and the second paints the four squares (4,1), (3,2), (2,3), (1,4) black.
Thus, the above output should be printed, since P=1, Q=5, R=1, S=5.

Sample Input 2

5 3 3
4 5 2 5

Sample Output 2

#.#.
...#

The operations paint the nine squares (1,1), (1,5), (2,2), (2,4), (3,3), (4,2), (4,4), (5,1), (5,5).
Thus, the above output should be printed, since P=4, Q=5, R=2, S=5.

Sample Input 3

1000000000000000000 999999999999999999 999999999999999999
999999999999999998 1000000000000000000 999999999999999998 1000000000000000000

Sample Output 3

#.#
.#.
#.#

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