The matrix A 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 maximum in its column.
Find the number of saddle points in a given matrix.
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 Aij. All Aij do not exceed 1000 by absolute value.
Print the number of saddle points.