Competitions
Week 12: February 8 - 14
Saddle points
The matrix K is given. It contains n rows and m columns. The saddle point of the matrix is an element that is minimum in its row and the maximum in its column.
Find the number of saddle points in a given matrix.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 750). Then given n rows with m numbers in each. The j-th number of the i-th line equals to kij. All kij do not exceed 1000 by absolute value.
Output
Print the number of saddle points.
Input example #1
2 2 0 0 0 0
Output example #1
4
Input example #2
3 4 7 1 5 3 3 2 6 4 5 2 8 6
Output example #2
2