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The chess board industry has fallen on hard times and needs your help. It is a little-known fact that chess boards are made from the bark of the extremely rare Croatian Chess Board tree, (Biggus Mobydiccus). The bark of that tree is stripped and unwrapped into a huge rectangular sheet of chess board material. The rectangle is a grid of black and white squares.

Your task is to make as many large square chess boards as possible. A chess board is a piece of the bark that is a square, with sides parallel to the sides of the bark rectangle, with cells colored in the pattern of a chess board (no two cells of the same color can share an edge).

Each time you cut out a chess board, you must choose the largest possible chess board left in the sheet. If there are several such boards, pick the topmost one. If there is still a tie, pick the leftmost one. Continue cutting out chess boards until there is no bark left. You may need to go as far as cutting out 1-by-1 mini chess boards.

Here is an example showing the bark of a Chess Board tree and the first few chess boards that will be cut out of it.

Input

The first line of the input gives the number of test cases, T. T test cases follow. Each one starts with a line containing the dimensions of the bark grid, M and N. N will always be a multiple of 4. The next M lines will each contain an (N/4)-character hexadecimal integer, representing a row of the bark grid. The binary representation of these integers will give you a strings of N bits, one for each row. Zeros represent black squares; ones represent white squares of the grid. The rows are given in the input from top to bottom. In each row, the most-significant bit of the hexadecimal integer corresponds to the leftmost cell in that row.

Output

For each test case, output one line containing "Case #x: K", where x is the case number (starting from 1) and K is the number of different chess board sizes that you can cut out by following the procedure described above. The next K lines should contain two integers each -- the size of the chess board (from largest to smallest) and the number of chess boards of that size that you can cut out.

Limits

1 ≤ T ≤ 100;
N will be divisible by 4;
Each hexadecimal integer will contain exactly N/4 characters.
Only the characters 0-9 and A-F will be used.

The input file will be at most 200kB in size.

Example

Input:
 4
 15 20
 55555
 FFAAA
 2AAD5
 D552A
 2AAD5
 D542A
 4AD4D
 B52B2
 52AAD
 AD552
 AA52D
 AAAAA
 5AA55
 A55AA
 5AA55
 4 4
 0
 0
 0
 0
 4 4
 3
 3
 C
 C
 4 4
 6
 9
 9
 6

Output:
 Case #1: 5
 6 2
 4 3
 3 7
 2 15
 1 57
 Case #2: 1
 1 16
 Case #3: 2
 2 1
 1 12
 Case #4: 1
 2 4