E. Empty Rectanglestime limit per test12 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou'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. InputThe 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.OutputPrint 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 С++. It is preferred to use the cin, cout streams or the %I64d specifier.ExamplesInput3 3 2101000101Output8Input5 5 10000000000001000000000000Output81Input5 5 60101010101010101010101010Output12Input3 3 0001010000Output15Input4 4 00000010100000000Output52
Input3 3 2101000101
Output8
['divide and conquer', 'two pointers', '*3000']