Balanced Path

AtCoder

IDabc147_e

Time2000ms

Memory256MB

Difficulty—

We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i,j)$ denote the square at the $i$\-th row from the top and the $j$\-th column from the left. The square $(i, j)$ has two numbers $A_{ij}$ and $B_{ij}$ written on it. First, for each square, Takahashi paints one of the written numbers red and the other blue. Then, he travels from the square $(1, 1)$ to the square $(H, W)$. In one move, he can move from a square $(i, j)$ to the square $(i+1, j)$ or the square $(i, j+1)$. He must not leave the grid. Let the _unbalancedness_ be the absolute difference of the sum of red numbers and the sum of blue numbers written on the squares along Takahashi's path, including the squares $(1, 1)$ and $(H, W)$. Takahashi wants to make the unbalancedness as small as possible by appropriately painting the grid and traveling on it. Find the minimum unbalancedness possible. ## Constraints * $2 \leq H \leq 80$ * $2 \leq W \leq 80$ * $0 \leq A_{ij} \leq 80$ * $0 \leq B_{ij} \leq 80$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $H$ $W$ $A_{11}$ $A_{12}$ $\ldots$ $A_{1W}$ $:$ $A_{H1}$ $A_{H2}$ $\ldots$ $A_{HW}$ $B_{11}$ $B_{12}$ $\ldots$ $B_{1W}$ $:$ $B_{H1}$ $B_{H2}$ $\ldots$ $B_{HW}$ [samples]

Samples

Input #1

Output #1

0

By painting the grid and traveling on it as shown in the figure below, the sum of red numbers and the sum of blue numbers are $3+3+1=7$ and $1+2+4=7$, respectively, for the unbalancedness of $0$.
![image](https://img.atcoder.jp/ghi/a7eefcd144e470dad1d3f833a6806f2c.png)

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Balanced Path",
    "description": {
      "content": "We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left. The square $(i, j)$ has two number",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc147_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a grid with $H$ horizontal rows and $W$ vertical columns. Let $(i,j)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left.\nThe square $(i, j)$ has two number...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments