Problem Statement

There is a triangle ABC with positive area.
The lengths of the three sides of triangle ABC are a,b,c.

Determine whether triangle ABC is isosceles.

Constraints

• 1 \leq a,b,c \leq 10
• A triangle with side lengths a,b,c exists, and its area is positive.
• a,b,c are integers.

Sample Input 1

4 2 4

Sample Output 1

Yes

Since a=c, triangle ABC is isosceles. Thus, output Yes.

Sample Input 2

3 4 5

Sample Output 2

No

Since the three side lengths of triangle ABC are all different, it is not isosceles. Thus, output No.

Sample Input 3

10 10 10

Sample Output 3

Yes

Note that an equilateral triangle is a kind of isosceles triangle.

Problem Statement

Takahashi had a report whose deadline was B minutes past A o'clock on May 17, 2025. He submitted it at D minutes past C o'clock on May 17, 2025.
It is guaranteed that "B minutes past A o'clock" and "D minutes past C o'clock" are different times.

Output Yes if Takahashi submitted the report before the deadline, and No otherwise.

Constraints

• 0 \leq A, C \leq 23
• 0 \leq B, D \leq 59
• (A, B) \neq (C, D)
• A, B, C, and D are integers.

Sample Input 1

22 40 22 30

Sample Output 1

Yes

The deadline is 22:40, and he submitted at 22:30, so he submitted before the deadline. Hence, output Yes.

Sample Input 2

22 40 22 45

Sample Output 2

No

The deadline is 22:40, and he submitted at 22:45, so he submitted after the deadline. Hence, output No.

Sample Input 3

12 0 11 30

Sample Output 3

Yes

Problem Statement

We have a board with R rows running horizontally and C columns running vertically. Let (i,j) denote the square at the i-th row from the top and j-th column from the left.

You are given characters B_{i,j} representing the current states of (i,j). . represents an empty square; # represents a square with a wall; 1, 2,\dots, 9 represent a square with a bomb of power 1,2,\dots,9, respectively.

At the next moment, all bombs will explode simultaneously. When a bomb explodes, every square whose Manhattan distance from the square with the bomb is not greater than the power of the bomb will turn into an empty square. Here, the Manhattan distance from (r_1,c_1) to (r_2,c_2) is |r_1-r_2|+|c_1-c_2|.

Print the board after the explosions.

Constraints

• 1\leq R,C \leq 20
• R and C are integers.
• Each B_{i,j} is one of ., #, 1, 2, \dots, 9.

Sample Input 1

4 4
.1.#
###.
.#2.
#.##

Sample Output 1

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

• The explosion of the bomb at (1,2) will turn the blue squares and purple squares in the above figure into empty squares.
• The explosion of the bomb at (3,3) will turn the red squares and purple squares in the above figure into empty squares.

As seen in this sample, the explosion ranges of bombs may overlap.

Sample Input 2

2 5
..#.#
###.#

Sample Output 2

..#.#
###.#

There may be no bombs.

Sample Input 3

2 3
11#
###

Sample Output 3

...
..#

Sample Input 4

4 6
#.#3#.
###.#.
##.###
#1..#.

Sample Output 4

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

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

You are given a matrix A with H_1 rows and W_1 columns, and a matrix B with H_2 rows and W_2 columns.

• For all integer pairs (i, j) such that 1 \leq i \leq H_1 and 1 \leq j \leq W_1, the element at the i-th row and j-th column of matrix A is A_{i, j}.
• For all integer pairs (i, j) such that 1 \leq i \leq H_2 and 1 \leq j \leq W_2, the element at the i-th row and j-th column of matrix B is B_{i, j}.

You may perform the following operations on the matrix A any number of (possibly 0) times in any order:

• Choose an arbitrary row of A and remove it.
• Choose an arbitrary column of A and remove it.

Determine if it is possible to make the matrix A equal the matrix B.

Constraints

• 1 \leq H_2 \leq H_1 \leq 10
• 1 \leq W_2 \leq W_1 \leq 10
• 1 \leq A_{i, j} \leq 10^9
• 1 \leq B_{i, j} \leq 10^9
• All values in input are integers.

Sample Input 1

4 5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
2 3
6 8 9
16 18 19

Sample Output 1

Yes

Removing the 2-nd column from the initial A results in:

1 3 4 5
6 8 9 10
11 13 14 15
16 18 19 20

Then, removing the 3-rd row from A results in:

1 3 4 5
6 8 9 10
16 18 19 20

Then, removing the 1-st row from A results in:

6 8 9 10
16 18 19 20

Then, removing the 4-th column from A results in:

6 8 9
16 18 19

Now the matrix equals the matrix B.
Thus, we can make the matrix A equal the matrix B by repeating the operations, so Yes should be printed.

Sample Input 2

3 3
1 1 1
1 1 1
1 1 1
1 1
2

Sample Output 2

No

Regardless of how we perform the operations, we cannot make the matrix A equal the matrix B, so No should be printed.