Binary Table

## 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

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?

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'.

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

3 4
0110
1010
0111

2