Problem Statement

AtCoder Beginner Contest usually starts at 21:00 JST and lasts for 100 minutes.

You are given an integer K between 0 and 100 (inclusive). Print the time K minutes after 21:00 in the HH:MM format, where HH denotes the hour on the 24-hour clock and MM denotes the minute. If the hour or the minute has just one digit, append a 0 to the beginning to represent it as a 2-digit integer.

Constraints

• K is an integer between 0 and 100 (inclusive).

Sample Input 1

63

Sample Output 1

22:03

63 minutes after 21:00, it will be 22:03, so 22:03 should be printed.

The following outputs would be judged incorrect:

• 10:03
• 22:3

Sample Input 2

45

Sample Output 2

21:45

Sample Input 3

100

Sample Output 3

22:40

Problem Statement

There are N people numbered 1, 2, \ldots, N, sitting in this clockwise order around a round table. In particular, person 1 is sitting next to person N in the clockwise direction.

For each i = 1, 2, \ldots, N, person i has a name S_i and an age A_i. Here, no two people have the same name or the same age.

Starting from the youngest person, print the names of all N people in the order of their seating positions in clockwise order.

Constraints

• 2 \leq N \leq 100
• N is an integer.
• S_i is a string of length between 1 and 10, consisting of lowercase English letters.
• i \neq j \implies S_i \neq S_j
• 0 \leq A_i \leq 10^9
• A_i is an integer.
• i \neq j \implies A_i \neq A_j

Sample Input 1

5
alice 31
bob 41
carol 5
dave 92
ellen 65

Sample Output 1

carol
dave
ellen
alice
bob

The youngest person is person 3. Therefore, starting from person 3, print the names in the clockwise order of their seating positions: person 3, person 4, person 5, person 1, and person 2.

Sample Input 2

2
takahashi 1000000000
aoki 999999999

Sample Output 2

aoki
takahashi

Problem Statement

We have a grid with H horizontal rows and W vertical columns, where each square contains an integer. The integer written on the square at the i-th row from the top and j-th column from the left is A_{i, j}.

Determine whether the grid satisfies the condition below.

A_{i_1, j_1} + A_{i_2, j_2} \leq A_{i_2, j_1} + A_{i_1, j_2} holds for every quadruple of integers (i_1, i_2, j_1, j_2) such that 1 \leq i_1 < i_2 \leq H and 1 \leq j_1 < j_2 \leq W.

Constraints

• 2 \leq H, W \leq 50
• 1 \leq A_{i, j} \leq 10^9
• All values in input are integers.

Sample Input 1

3 3
2 1 4
3 1 3
6 4 1

Sample Output 1

Yes

There are nine quadruples of integers (i_1, i_2, j_1, j_2) such that 1 \leq i_1 < i_2 \leq H and 1 \leq j_1 < j_2 \leq W. For all of them, A_{i_1, j_1} + A_{i_2, j_2} \leq A_{i_2, j_1} + A_{i_1, j_2} holds. Some examples follow.

• For (i_1, i_2, j_1, j_2) = (1, 2, 1, 2), we have A_{i_1, j_1} + A_{i_2, j_2} = 2 + 1 \leq 3 + 1 = A_{i_2, j_1} + A_{i_1, j_2}.
• For (i_1, i_2, j_1, j_2) = (1, 2, 1, 3), we have A_{i_1, j_1} + A_{i_2, j_2} = 2 + 3 \leq 3 + 4 = A_{i_2, j_1} + A_{i_1, j_2}.
• For (i_1, i_2, j_1, j_2) = (1, 2, 2, 3), we have A_{i_1, j_1} + A_{i_2, j_2} = 1 + 3 \leq 1 + 4 = A_{i_2, j_1} + A_{i_1, j_2}.
• For (i_1, i_2, j_1, j_2) = (1, 3, 1, 2), we have A_{i_1, j_1} + A_{i_2, j_2} = 2 + 4 \leq 6 + 1 = A_{i_2, j_1} + A_{i_1, j_2}.
• For (i_1, i_2, j_1, j_2) = (1, 3, 1, 3), we have A_{i_1, j_1} + A_{i_2, j_2} = 2 + 1 \leq 6 + 4 = A_{i_2, j_1} + A_{i_1, j_2}.

We can also see that the property holds for the other quadruples: (i_1, i_2, j_1, j_2) = (1, 3, 2, 3), (2, 3, 1, 2), (2, 3, 1, 3), (2, 3, 2, 3).
Thus, we should print Yes.

Sample Input 2

2 4
4 3 2 1
5 6 7 8

Sample Output 2

No

We should print No because the condition is not satisfied.
This is because, for example, we have A_{i_1, j_1} + A_{i_2, j_2} = 4 + 8 > 5 + 1 = A_{i_2, j_1} + A_{i_1, j_2} for (i_1, i_2, j_1, j_2) = (1, 2, 1, 4).

Problem Statement

You are given N strings of length six each, consisting of digits. Let S_i be the i-th (i = 1, 2, \dots, N) of them.

You are also given M strings of length three each, consisting of digits. Let T_j be the j-th (j = 1, 2, \dots, M) of them.

Find the number of strings among S_1, S_2, \dots, S_N whose last three characters coincide with one or more of T_1, T_2, \dots, T_M.

Constraints

• 1 \leq N, M \leq 1000
• N and M are integers.
• S_i is a string of length 6 consisting of digits, for all i = 1, 2, \dots, N.
• T_j is a string of length 3 consisting of digits, for all j = 1, 2, \dots, M.

Sample Input 1

3 3
142857
004159
071028
159
287
857

Sample Output 1

2

The last three characters of S_1 are 857, which coincide with T_3.
The last three characters of S_2 are 159, which coincide with T_1.
The last three characters of S_3 are 028, which do not coincide with T_1, T_2, or T_3.

Thus, the answer is 2.

Sample Input 2

5 4
235983
109467
823476
592801
000333
333
108
467
983

Sample Output 2

3

Sample Input 3

4 4
000000
123456
987111
000000
000
111
999
111

Sample Output 3

3

Problem Statement

We have a grid with H horizontal rows and W vertical columns. We denote by (i, j) the cell at the i-th row from the top and j-th column from the left of the grid.
Each cell in the grid has a symbol # or . written on it. Let C[i][j] be the character written on (i, j). For integers i and j such that at least one of 1 \leq i \leq H and 1 \leq j \leq W is violated, we define C[i][j] to be ..

(4n+1) squares, consisting of (a, b) and (a+d,b+d),(a+d,b-d),(a-d,b+d),(a-d,b-d) (1 \leq d \leq n, 1 \leq n), are said to be a cross of size n centered at (a,b) if and only if all of the following conditions are satisfied:

• C[a][b] is #.
• C[a+d][b+d],C[a+d][b-d],C[a-d][b+d], and C[a-d][b-d] are all #, for all integers d such that 1 \leq d \leq n,
• At least one of C[a+n+1][b+n+1],C[a+n+1][b-n-1],C[a-n-1][b+n+1], and C[a-n-1][b-n-1] is ..

For example, the grid in the following figure has a cross of size 1 centered at (2, 2) and another of size 2 centered at (3, 7).

The grid has some crosses. No # is written on the cells except for those comprising a cross.
Additionally, no two squares that comprise two different crosses share a corner. The two grids in the following figure are the examples of grids where two squares that comprise different crosses share a corner; such grids are not given as an input. For example, the left grid is invalid because (3, 3) and (4, 4) share a corner.

Let N = \min(H, W), and S_n be the number of crosses of size n. Find S_1, S_2, \dots, S_N.

Constraints

• 3 \leq H, W \leq 100
• C[i][j] is # or ..
• No two different squares that comprise two different crosses share a corner.
• H and W are integers.

Sample Input 1

5 9
#.#.#...#
.#...#.#.
#.#...#..
.....#.#.
....#...#

Sample Output 1

1 1 0 0 0

As described in the Problem Statement, there are a cross of size 1 centered at (2, 2) and another of size 2 centered at (3, 7).

Sample Input 2

3 3
...
...
...

Sample Output 2

0 0 0

There may be no cross.

Sample Input 3

3 16
#.#.....#.#..#.#
.#.......#....#.
#.#.....#.#..#.#

Sample Output 3

3 0 0

Sample Input 4

15 20
#.#..#.............#
.#....#....#.#....#.
#.#....#....#....#..
........#..#.#..#...
#.....#..#.....#....
.#...#....#...#..#.#
..#.#......#.#....#.
...#........#....#.#
..#.#......#.#......
.#...#....#...#.....
#.....#..#.....#....
........#.......#...
#.#....#....#.#..#..
.#....#......#....#.
#.#..#......#.#....#

Sample Output 4

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

Problem Statement

How many integer sequences of length N, A=(A_1, \ldots, A_N), satisfy all of the conditions below?

• 1\le A_i \le M (1 \le i \le N)

• \displaystyle\sum _{i=1}^N A_i \leq K

Since the count can get enormous, find it modulo 998244353.

Constraints

• 1 \leq N, M \leq 50
• N \leq K \leq NM
• All values in input are integers.

Sample Input 1

2 3 4

Sample Output 1

6

The following six sequences satisfy the conditions.

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

Sample Input 2

31 41 592

Sample Output 2

798416518

Be sure to print the count modulo 998244353.

Problem Statement

There is a grid with N \times N squares. We denote by (i, j) the square at the i-th row from the top and j-th column from the left.

Initially, a piece is placed on (1, 1). You may repeat the following operation any number of times:

• Let (i, j) be the square the piece is currently on. Move the piece to the square whose distance from (i, j) is exactly \sqrt{M}.

Here, we define the distance between square (i, j) and square (k, l) as \sqrt{(i-k)^2+(j-l)^2}.

For all squares (i, j), determine if the piece can reach (i, j). If it can, find the minimum number of operations required to do so.

Constraints

• 1 \le N \le 400
• 1 \le M \le 10^6
• All values in the input are integers.

Sample Input 1

3 1

Sample Output 1

0 1 2
1 2 3
2 3 4

You can move the piece to four adjacent squares.

For example, we can move the piece to (2,2) with two operations as follows.

• The piece is now on (1,1). The distance between (1,1) and (1,2) is exactly \sqrt{1}, so move the piece to (1,2).
• The piece is now on (1,2). The distance between (1,2) and (2,2) is exactly \sqrt{1}, so move the piece to (2,2).

Sample Input 2

10 5

Sample Output 2

0 3 2 3 2 3 4 5 4 5
3 4 1 2 3 4 3 4 5 6
2 1 4 3 2 3 4 5 4 5
3 2 3 2 3 4 3 4 5 6
2 3 2 3 4 3 4 5 4 5
3 4 3 4 3 4 5 4 5 6
4 3 4 3 4 5 4 5 6 5
5 4 5 4 5 4 5 6 5 6
4 5 4 5 4 5 6 5 6 7
5 6 5 6 5 6 5 6 7 6

Problem Statement

We have a grid with 2 rows and L columns. Let (i,j) denote the square at the i-th row from the top (i\in\lbrace1,2\rbrace) and j-th column from the left (1\leq j\leq L). (i,j) has an integer x _ {i,j} written on it.

Find the number of integers j such that x _ {1,j}=x _ {2,j}.

Here, the description of x _ {i,j} is given to you as the run-length compressions of (x _ {1,1},x _ {1,2},\ldots,x _ {1,L}) and (x _ {2,1},x _ {2,2},\ldots,x _ {2,L}) into sequences of lengths N _ 1 and N _ 2, respectively: ((v _ {1,1},l _ {1,1}),\ldots,(v _ {1,N _ 1},l _ {1,N _ 1})) and ((v _ {2,1},l _ {2,1}),\ldots,(v _ {2,N _ 2},l _ {2,N _ 2})).

Here, the run-length compression of a sequence A is a sequence of pairs (v _ i,l _ i) of an element v _ i of A and a positive integer l _ i obtained as follows.

1. Split A between each pair of different adjacent elements.
2. For each sequence B _ 1,B _ 2,\ldots,B _ k after the split, let v _ i be the element of B _ i and l _ i be the length of B _ i.

Constraints

• 1\leq L\leq 10 ^ {12}
• 1\leq N _ 1,N _ 2\leq 10 ^ 5
• 1\leq v _ {i,j}\leq 10 ^ 9\ (i\in\lbrace1,2\rbrace,1\leq j\leq N _ i)
• 1\leq l _ {i,j}\leq L\ (i\in\lbrace1,2\rbrace,1\leq j\leq N _ i)
• v _ {i,j}\neq v _ {i,j+1}\ (i\in\lbrace1,2\rbrace,1\leq j\lt N _ i)
• l _ {i,1}+l _ {i,2}+\cdots+l _ {i,N _ i}=L\ (i\in\lbrace1,2\rbrace)
• All values in the input are integers.

Sample Input 1

8 4 3
1 2
3 2
2 3
3 1
1 4
2 1
3 3

Sample Output 1

4

The grid is shown below.

We have four integers j such that x _ {1,j}=x _ {2,j}: j=1,2,5,8. Thus, you should print 4.

Sample Input 2

10000000000 1 1
1 10000000000
1 10000000000

Sample Output 2

10000000000

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

Sample Input 3

1000 4 7
19 79
33 463
19 178
33 280
19 255
33 92
34 25
19 96
12 11
19 490
33 31

Sample Output 3

380

Problem Statement

Takahashi is on an xy-plane. Initially, he is at point (s _ x,s _ y), and he wants to reach point (t _ x,t _ y).

On the xy-plane is a rectangle R\coloneqq\lbrace(x,y)\mid a-0.5\leq x\leq b+0.5,c-0.5\leq y\leq d+0.5\rbrace. Consider the following operation:

• Choose a lattice point (x,y) contained in the rectangle R. Takahashi teleports to the point symmetric to his current position with respect to point (x,y).

Determine if he can reach point (t _ x,t _ y) after repeating the operation above between 0 and 10^6 times, inclusive. If it is possible, construct a sequence of operations that leads him to point (t _ x,t _ y).

Constraints

• 0\leq s _ x,s _ y,t _ x,t _ y\leq2\times10^5
• 0\leq a\leq b\leq2\times10^5
• 0\leq c\leq d\leq2\times10^5
• All values in the input are integers.

Sample Input 1

1 2
7 8
7 9 0 3

Sample Output 1

Yes
7 0
9 3
7 1
8 1

For example, the following choices lead him from (1,2) to (7,8).

• Choose (7,0). Takahashi moves to (13,-2).
• Choose (9,3). Takahashi moves to (5,8).
• Choose (7,1). Takahashi moves to (9,-6).
• Choose (8,1). Takahashi moves to (7,8).

Any output that satisfies the conditions is accepted; for example, printing

Yes
7 3
9 0
7 2
9 1
8 1

is also accepted.

Sample Input 2

0 0
8 4
5 5 0 0

Sample Output 2

No

No sequence of operations leads him to point (8,4).

Sample Input 3

1 4
1 4
100 200 300 400

Sample Output 3

Yes

Takahashi may already be at the destination in the beginning.

Sample Input 4

22 2
16 7
14 30 11 14

Sample Output 4

No