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 `k`

. All _{ij}`k`

do not exceed _{ij}**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