Binary Table

题意翻译

## 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?

输入输出格式

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.

输入输出样例

输入样例 #1

3 4
0110
1010
0111

输出样例 #1

2