Add to Square

AtCoder

IDarc135_d

Time2000ms

Memory256MB

Difficulty—

We have an $H \times W$ grid, where each square has one integer written on it. For $1\leq i\leq H$ and $1\leq j\leq W$, let $A_{i,j}$ denote the integer written on the square at the $i$\-th row and $j$\-th column. You can do the operation below any number of times (possibly zero). * Choose integers $i$ and $j$ such that $1\leq i\leq H - 1$ and $1\leq j\leq W - 1$. * Choose another integer $x$. * Add $x$ to each of $A_{i,j}$, $A_{i,j+1}$, $A_{i+1,j}$, and $A_{i+1,j+1}$. Print the minimum possible value of $\sum_{i=1}^H \sum_{j=1}^W |A_{i,j}|$ after your operations, and the integers on the grid when that value is achieved. ## Constraints * $2\leq H, W \leq 500$ * $|A_{i,j}|\leq 10^9$ ## Input Input is given from Standard Input from the following format: $H$ $W$ $A_{1,1}$ $\ldots$ $A_{1,W}$ $\vdots$ $A_{H,1}$ $\ldots$ $A_{H,W}$ [samples]

Samples

Input #1

2 3
1 2 3
4 5 6

Output #1

9
0 -3 -1
3 0 2

Here is a sequence of operations that produces the grid in the Sample Output.

*   Do the operation with $(i, j, x) = (1, 1, -1)$.
*   Do the operation with $(i, j, x) = (1, 2, -4)$.

Here, we have $\sum_{i=1}^H \sum_{j=1}^W |A_{i,j}| = 0 + 3 + 1 + 3 + 0 + 2 = 9$.

Input #2

2 2
1000000000 -1000000000
-1000000000 1000000000

Output #2

4000000000
2000000000 0
0 2000000000

It is fine if $|A_{i,j}| > 10^9$ after your operations.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Add to Square",
    "description": {
      "content": "We have an $H \\times W$ grid, where each square has one integer written on it. For $1\\leq i\\leq H$ and $1\\leq j\\leq W$, let $A_{i,j}$ denote the integer written on the square at the $i$\\-th row and $j",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc135_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an $H \\times W$ grid, where each square has one integer written on it. For $1\\leq i\\leq H$ and $1\\leq j\\leq W$, let $A_{i,j}$ denote the integer written on the square at the $i$\\-th row and $j...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments