Problem Statement

You are given three strings S_1, S_2, S_3 consisting of lowercase English letters, and a string T consisting of 1, 2, 3.

Concatenate the three strings according to the characters in T and print the resulting string. Formally, conform to the following instructions.

• For each integer i such that 1 \leq i \leq |T|, let the string s_i be defined as follows:
  • S_1, if the i-th character of T is 1;
  • S_2, if the i-th character of T is 2;
  • S_3, if the i-th character of T is 3.
• Concatenate the strings s_1, s_2, \dots, s_{|T|} in this order and print the resulting string.

Constraints

• 1 \leq |S_1|, |S_2|, |S_3| \leq 10
• 1 \leq |T| \leq 1000
• S_1, S_2, and S_3 consist of lowercase English letters.
• T consists of 1, 2, and 3.

Sample Input 1

mari
to
zzo
1321

Sample Output 1

marizzotomari

We have s_1 = mari, s_2 = zzo, s_3 = to, s_4 = mari. Concatenate these and print the resulting string: marizzotomari.

Sample Input 2

abra
cad
abra
123

Sample Output 2

abracadabra

Sample Input 3

a
b
c
1

Sample Output 3

a

Problem Statement

We have a sequence of length N consisting of positive integers: A=(A_1,\ldots,A_N). Any two adjacent terms have different values.

Let us insert some numbers into this sequence by the following procedure.

1. If every pair of adjacent terms in A has an absolute difference of 1, terminate the procedure.
2. Let A_i, A_{i+1} be the pair of adjacent terms nearest to the beginning of A whose absolute difference is not 1.
   • If A_i < A_{i+1}, insert A_i+1,A_i+2,\ldots,A_{i+1}-1 between A_i and A_{i+1}.
   • If A_i > A_{i+1}, insert A_i-1,A_i-2,\ldots,A_{i+1}+1 between A_i and A_{i+1}.
3. Return to step 1.

Print the sequence when the procedure ends.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 100
• A_i \neq A_{i+1}
• All values in the input are integers.

Sample Input 1

4
2 5 1 2

Sample Output 1

2 3 4 5 4 3 2 1 2

The initial sequence is (2,5,1,2). The procedure goes as follows.

• Insert 3,4 between the first term 2 and the second term 5, making the sequence (2,3,4,5,1,2).
• Insert 4,3,2 between the fourth term 5 and the fifth term 1, making the sequence (2,3,4,5,4,3,2,1,2).

Sample Input 2

6
3 4 5 6 5 4

Sample Output 2

3 4 5 6 5 4

No insertions may be performed.

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

You are given patterns S and T consisting of # and ., each with H rows and W columns.
The pattern S is given as H strings, and the j-th character of S_i represents the element at the i-th row and j-th column. The same goes for T.

Determine whether S can be made equal to T by rearranging the columns of S.

Here, rearranging the columns of a pattern X is done as follows.

• Choose a permutation P=(P_1,P_2,\dots,P_W) of (1,2,\dots,W).
• Then, for every integer i such that 1 \le i \le H, simultaneously do the following.
  • For every integer j such that 1 \le j \le W, simultaneously replace the element at the i-th row and j-th column of X with the element at the i-th row and P_j-th column.

Constraints

• H and W are integers.
• 1 \le H,W
• 1 \le H \times W \le 4 \times 10^5
• S_i and T_i are strings of length W consisting of # and ..

Sample Input 1

3 4
##.#
##..
#...
.###
..##
...#

Sample Output 1

Yes

If you, for instance, arrange the 3-rd, 4-th, 2-nd, and 1-st columns of S in this order from left to right, S will be equal to T.

Sample Input 2

3 3
#.#
.#.
#.#
##.
##.
.#.

Sample Output 2

No

In this input, S cannot be made equal to T.

Sample Input 3

2 1
#
.
#
.

Sample Output 3

Yes

It is possible that S=T.

Sample Input 4

8 7
#..#..#
.##.##.
#..#..#
.##.##.
#..#..#
.##.##.
#..#..#
.##.##.
....###
####...
....###
####...
....###
####...
....###
####...

Sample Output 4

Yes

Problem Statement

You are given positive integers A and B.

You will repeat the following operation until A=B:

• compare A and B to perform one of the following two:
  • if A > B, replace A with A-B;
  • if A < B, replace B with B-A.

How many times will you repeat it until A=B? It is guaranteed that a finite repetition makes A=B.

Constraints

• 1 \le A,B \le 10^{18}
• All values in the input are integers.

Sample Input 1

3 8

Sample Output 1

4

Initially, A=3 and B=8. You repeat the operation as follows:

• A<B, so replace B with B-A=5, making A=3 and B=5.
• A<B, so replace B with B-A=2, making A=3 and B=2.
• A>B, so replace A with A-B=1, making A=1 and B=2.
• A<B, so replace B with B-A=1, making A=1 and B=1.

Thus, you repeat it four times.

Sample Input 2

1234567890 1234567890

Sample Output 2

0

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

Sample Input 3

1597 987

Sample Output 3

15