CF375B.Maximum Submatrix 2

You are given a matrix consisting of digits zero and one, its size is n × m. You are allowed to rearrange its rows. What is the maximum area of the submatrix that only consists of ones and can be obtained in the given problem by the described operations?

Let's assume that the rows of matrix a are numbered from 1 to n from top to bottom and the columns are numbered from 1 to m from left to right. A matrix cell on the intersection of the i-th row and the j-th column can be represented as (i, j). Formally, a submatrix of matrix a is a group of four integers d, u, l, r (1 ≤ d ≤ u ≤ n; 1 ≤ l ≤ r ≤ m). We will assume that the submatrix contains cells (i, j) (d ≤ i ≤ u; l ≤ j ≤ r). The area of the submatrix is the number of cells it contains.

给你一个由数字 0 和 1 构成的矩阵，其大小为 $ n \times m $。你可以任意重排该矩阵的行。在执行上述操作后，所能得到的全由 1 组成的子矩阵的最大面积是多少？

假设矩阵 $ a $ 的行从上到下编号为 $ 1 $ 到 $ n $，列从左到右编号为 $ 1 $ 到 $ m $。位于第 $ i $ 行、第 $ j $ 列的矩阵单元格可表示为 $ (i,,j) $。形式化地，矩阵 $ a $ 的一个子矩阵由四个整数 $ d,,u,,l,,r $（满足 $ 1 \le d \le u \le n $；$ 1 \le l \le r \le m $）确定。我们规定该子矩阵包含所有满足 $ d \le i \le u $ 且 $ l \le j \le r $ 的单元格 $ (i,,j) $。该子矩阵的面积即为其所含单元格的总数。

The first line contains two integers n and m (1 ≤ n, m ≤ 5000). Next n lines contain m characters each — matrix a. Matrix a only contains characters: "0" and "1". Note that the elements of the matrix follow without any spaces in the lines.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n, m \leq 5000$）。接下来的 $n$ 行，每行包含 $m$ 个字符，构成矩阵 $a$。矩阵 $a$ 仅包含字符 "0" 和 "1"。注意：每行中的矩阵元素之间不包含任何空格。

Print a single integer — the area of the maximum obtained submatrix. If we cannot obtain a matrix of numbers one, print 0.

输出一个整数——所得最大子矩阵的面积。如果我们无法得到一个全为数字 1 的矩阵，则输出 0。