Coin Flips

Coins are placed on an N×M grid. Both N and M are odd. A coin showing heads is written as 0, and a coin showing tails is written as 1.

In one operation, choose exactly one row or one column and flip every coin in it. A flipped coin changes from 0 to 1 or from 1 to 0.

Your goal is to make the number of 1s even in every row and every column. Find the minimum number of operations needed.

The first line contains the height N and width M of the grid. N and M are odd integers not greater than 1,000.

Each of the next N lines contains a string of length M. Every character is either 0 or 1 and describes the current state of the coins.

Print the minimum number of operations needed to make the number of 1s even in every row and every column. If it is impossible, print -1.

In the first public test, flipping the middle row and the middle column satisfies the condition.