Description

Teacher Mai has a board of n rows and m columns. There is a light in each cell.

He can flip some lights: if this light is on, turn it off, else turn it on.

He can choose a cell(i,j), and he has following two operations:

1. Flip the light on the cells which share a common edge with cell(i,j).
2. Flip the light on the cells which share a common edge with cell(i,j) and cell(i,j).

You are given the initial state of board. Output the minimum operations to turn off the all the lights.

Format

Input

There are multiple test cases, terminated by a line "0 0".

For each test case, the first line contains two integers n,m(1<=n,m<=10).

In following n lines, each line contains a string consisting of m characters, representing the initial state(0 means off, 1 means on).

Output

For each case, output "Case #k: ans" first, where k is the case number counting from 1, ans is the minimum operations.

Samples

3 3
111
111
111
3 3
000
010
000
0 0

Case #1: 3
Case #2: 2

Limitation