Problem Statement

You are given a string S of length N consisting of lowercase English letters.
We denote the i-th character of S by S_i.
Print the string of length 2N obtained by concatenating S_1,S_1,S_2,S_2,\dots,S_N, and S_N in this order.
For example, if S is beginner, print bbeeggiinnnneerr.

Constraints

• N is an integer such that 1 \le N \le 50.
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

8
beginner

Sample Output 1

bbeeggiinnnneerr

It is the same as the example described in the problem statement.

Sample Input 2

3
aaa

Sample Output 2

aaaaaa

Problem Statement

There are three brothers named A, B, and C. The age relationships among them are given by three characters S_{\mathrm{AB}}, S_{\mathrm{AC}}, S_{\mathrm{BC}}, which mean the following:

• If S_{\mathrm{AB}} is <, then A is younger than B; if it is >, then A is older than B.
• If S_{\mathrm{AC}} is <, then A is younger than C; if it is >, then A is older than C.
• If S_{\mathrm{BC}} is <, then B is younger than C; if it is >, then B is older than C.

Who is the middle brother, that is, the second oldest among the three?

Constraints

• Each of S_{\mathrm{AB}}, S_{\mathrm{AC}}, S_{\mathrm{BC}} is < or >.
• The input contains no contradictions; that is, there always exists an age relationship that satisfies all given inequalities.

Sample Input 1

< < <

Sample Output 1

B

Since A is younger than B, and B is younger than C, we can determine that C is the oldest, B is the middle, and A is the youngest. Hence, the answer is B.

Sample Input 2

< < >

Sample Output 2

C

Problem Statement

You are given two strings S and T consisting of lowercase English letters. The lengths of S and T are N and M, respectively. (The constraints guarantee that N \leq M.)

S is said to be a prefix of T when the first N characters of T coincide S.
S is said to be a suffix of T when the last N characters of T coincide S.

If S is both a prefix and a suffix of T, print 0;
If S is a prefix of T but not a suffix, print 1;
If S is a suffix of T but not a prefix, print 2;
If S is neither a prefix nor a suffix of T, print 3.

Constraints

• 1 \leq N \leq M \leq 100
• S is a string of length N consisting of lowercase English letters.
• T is a string of length M consisting of lowercase English letters.

Sample Input 1

3 7
abc
abcdefg

Sample Output 1

1

S is a prefix of T but not a suffix, so you should print 1.

Sample Input 2

3 4
abc
aabc

Sample Output 2

2

S is a suffix of T but not a prefix.

Sample Input 3

3 3
abc
xyz

Sample Output 3

3

S is neither a prefix nor a suffix of T.

Sample Input 4

3 3
aaa
aaa

Sample Output 4

0

S and T may coincide, in which case S is both a prefix and a suffix of T.

Problem Statement

You are given a positive integer N. Print a string of length (N+1), s_0s_1\ldots s_N, defined as follows.

For each i = 0, 1, 2, \ldots, N,

• if there is a divisor j of N that is between 1 and 9, inclusive, and i is a multiple of N/j, then s_i is the digit corresponding to the smallest such j (s_i will thus be one of 1, 2, ..., 9);
• if no such j exists, then s_i is -.

Constraints

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

Sample Input 1

12

Sample Output 1

1-643-2-346-1

We will explain how to determine s_i for some i.

• For i = 0, the divisors j of N between 1 and 9 such that i is a multiple of N/j are 1, 2, 3, 4, 6. The smallest of these is 1, so s_0 = 1.

• For i = 4, the divisors j of N between 1 and 9 such that i is a multiple of N/j are 3, 6. The smallest of these is 3, so s_4 = 3.

• For i = 11, there are no divisors j of N between 1 and 9 such that i is a multiple of N/j, so s_{11} = -.

Sample Input 2

7

Sample Output 2

17777771

Sample Input 3

1

Sample Output 3

11

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