Binary Table

题面翻译

题目描述

有一个 $n$ 行 $m$ 列的表格，每个元素都是 $0/1$ ，每次操作可以选择一行或一列，把 $0/1$ 翻转，即把 $0$ 换为 $1$ ，把 $1$ 换为 $0$ 。请问经过若干次操作后，表格中最少有多少个 $1$ 。

输入输出格式

输入格式:

第一行是两个整数 $n$ 和 $m$ （ $1\leqslant n\leqslant 20,1\leqslant m\leqslant 10^5$ ）之后 $n$ 行，每行 $m$ 个数字 $0/1$ ，注意数字间无空格。

输出格式:

一行，一个整数，表示答案。

感谢@AThousandMoon 提供翻译

题目描述

You are given a table consisting of $n$ rows and $m$ columns. Each cell of the table contains either $0$ or $1$ . In one move, you are allowed to pick any row or any column and invert all values, that is, replace $0$ by $1$ and vice versa.

What is the minimum number of cells with value 1 you can get after applying some number of operations?

输入格式

The first line of the input contains two integers $n$ and $m$ ( $1<=n<=20$ , $1<=m<=100000$ ) — the number of rows and the number of columns, respectively.

Then $n$ lines follows with the descriptions of the rows. Each line has length $m$ and contains only digits '0' and '1'.

输出格式

Output a single integer — the minimum possible number of ones you can get after applying some sequence of operations.

样例 #1

样例输入 #1

3 4
0110
1010
0111

样例输出 #1

2