One More Grid Task

AtCoder

IDabc311_g

Time3000ms

Memory256MB

Difficulty—

There is an $N \times M$ grid, where the square at the $i$\-th row from the top and $j$\-th column from the left has a non-negative integer $A_{i,j}$ written on it. Let us choose a rectangular region $R$. Formally, the region is chosen as follows. * Choose integers $l_x, r_x, l_y, r_y$ such that $1 \le l_x \le r_x \le N, 1 \le l_y \le r_y \le M$. * Then, square $(i,j)$ is in $R$ if and only if $l_x \le i \le r_x$ and $l_y \le j \le r_y$. Find the maximum possible value of $f(R) = $ (the sum of integers written on the squares in $R$) $\times$ (the smallest integer written on a square in $R$). ## Constraints * All input values are integers. * $1 \le N,M \le 300$ * $1 \le A_{i,j} \le 300$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_{1,1}$ $A_{1,2}$ $\dots$ $A_{1,M}$ $A_{2,1}$ $A_{2,2}$ $\dots$ $A_{2,M}$ $\vdots$ $A_{N,1}$ $A_{N,2}$ $\dots$ $A_{N,M}$ [samples]

Samples

Input #1

Output #1

48

Choosing the rectangular region whose top-left corner is square $(1, 1)$ and whose bottom-right corner is square $(2, 2)$ achieves $f(R) = (5+4+4+3) \times \min(5,4,4,3) = 48$, which is the maximum possible value.

Input #2

Output #2

Input #3

6 6
1 300 300 300 300 300
300 1 300 300 300 300
300 300 1 300 300 300
300 300 300 1 300 300
300 300 300 300 1 300
300 300 300 300 300 1

Output #3

API Response (JSON)

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    "name": "One More Grid Task",
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      "content": "There is an $N \\times M$ grid, where the square at the $i$\\-th row from the top and $j$\\-th column from the left has a non-negative integer $A_{i,j}$ written on it.   Let us choose a rectangular regio",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "sync_url": null,
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    {
      "statement_type": "Markdown",
      "content": "There is an $N \\times M$ grid, where the square at the $i$\\-th row from the top and $j$\\-th column from the left has a non-negative integer $A_{i,j}$ written on it.  \nLet us choose a rectangular regio...",
      "is_translate": false,
      "language": "English"
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