Problem3265--Empty Rectangles

3265: Empty Rectangles

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
12 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You've got an n×m table (n rows and m columns), each cell of the table contains a "0" or a "1".

Your task is to calculate the number of rectangles with the sides that are parallel to the sides of the table and go along the cell borders, such that the number one occurs exactly k times in the rectangle.

Input

The first line contains three space-separated integers n, m and k (1≤n,m≤2500, 0≤k≤6) − the sizes of the table and the required number of numbers one.

Next n lines each contains m characters "0" or "1". The i-th character of the j-th line corresponds to the character that is in the j-th row and the i-th column of the table.

Output

Print a single number − the number of rectangles that contain exactly k numbers one.

Please, do not write the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples
Input
3 3 2
101
000
101
Output
8
Input
5 5 1
00000
00000
00100
00000
00000
Output
81
Input
5 5 6
01010
10101
01010
10101
01010
Output
12
Input
3 3 0
001
010
000
Output
15
Input
4 4 0
0000
0101
0000
0000
Output
52

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