Problem Statement

There is a $H \times W$ grid, and each cell contains $0$ or $1$. The cell at the $i$-th row from the top and the $j$-th column from the left contains an integer $A_{i,j}$.

You can perform the following two operations any number of times in any order:

• Operation X: Choose an integer $x$ ($1 \leq x \leq H$). For every integer $1 \leq y \leq W$, replace $A_{x,y}$ with $1 - A_{x,y}$.
• Operation Y: Choose an integer $y$ ($1 \leq y \leq W$). For every integer $1 \leq x \leq H$, replace $A_{x,y}$ with $1 - A_{x,y}$.

Find the minimum possible value of $\displaystyle \sum_{x=1}^H\sum_{y=1}^W A_{x,y}$ after the process.

Constraints

• $1 \leq H \leq 2\times 10^5$
• $1 \leq W \leq 18$
• $H$ and $W$ are integers.
• $A_{i,1}A_{i,2}\ldots A_{i,W}$ is a length-$W$ string consisting of 0 and 1.

Input

The input is given from Standard Input in the following format:

H W
A_{1,1}A_{1,2}\ldots A_{1,W}
A_{2,1}A_{2,2}\ldots A_{2,W}
\vdots
A_{H,1}A_{H,2}\ldots A_{H,W}

Output

Print the answer.