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题目描述

Given a $N \times M$binary matrix. Please output the size of second large rectangle containing all $\texttt{"1"}$.

Containing all $\texttt{"1"}$ means that the entries of the rectangle are all $\texttt{"1"}$.

A rectangle can be defined as four integers $x_1, y_1, x_2, y_2$​ where $1 \leq x_1 \leq x_2 \leq N$and $1 \leq y_1 \leq y_2 \leq M$. Then, the rectangle is composed of all the cell (x, y) where $x_1 \leq x \leq x_2$and $y_1 \leq y \leq y2$. If all of the cell in the rectangle is $\texttt{"1"}$, this is a valid rectangle.

Please find out the size of the second largest rectangle, two rectangles are different if exists a cell belonged to one of them but not belonged to the other.

输入格式

The first line of input contains two space-separated integers N and M. Following N lines each contains M characters $c_{ij}$.

输出格式

Output one line containing an integer representing the answer. If there are less than 2 rectangles containning all "1"\texttt{"1"}"1", output $\texttt{"0"}$.

样例

样例输入 1

1 2
01

样例输出 1

0

样例输入 2

1 3
101

样例输出 2

1

数据范围与提示

1≤N,M≤1000

$N \times M \geq 2$

$c_{ij} \in \texttt{"01"}$