Competitions

# Week 12: February 8 - 14

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 (1n, m750). 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.

Time limit 2 seconds
Memory limit 128 MiB
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