Coloring Matrix

AtCoder

IDabc298_b

Time2000ms

Memory256MB

Difficulty—

You are given $N$\-by-$N$ matrices $A$ and $B$ where each element is $0$ or $1$. Let $A_{i,j}$ and $B_{i,j}$ denote the element at the $i$\-th row and $j$\-th column of $A$ and $B$, respectively. Determine whether it is possible to rotate $A$ so that $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$. Here, to rotate $A$ is to perform the following operation zero or more times: * for every pair of integers $(i, j)$ such that $1 \leq i, j \leq N$, simultaneously replace $A_{i,j}$ with $A_{N + 1 - j,i}$. ## Constraints * $1 \leq N \leq 100$ * Each element of $A$ and $B$ is $0$ or $1$. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,N}$ $\vdots$ $A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,N}$ $B_{1,1}$ $B_{1,2}$ $\ldots$ $B_{1,N}$ $\vdots$ $B_{N,1}$ $B_{N,2}$ $\ldots$ $B_{N,N}$ [samples]

Samples

Input #1

Output #1

Yes

Initially, $A$ is :

0 1 1
1 0 0
0 1 0

After performing the operation once, $A$ is :

0 1 0
1 0 1 
0 0 1

After performing the operation once again, $A$ is :

0 1 0
0 0 1
1 1 0

Here, $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$, so you should print `Yes`.

Input #2

Output #2

Yes

Input #3

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "Coloring Matrix",
    "description": {
      "content": "You are given $N$\\-by-$N$ matrices $A$ and $B$ where each element is $0$ or $1$.   Let $A_{i,j}$ and $B_{i,j}$ denote the element at the $i$\\-th row and $j$\\-th column of $A$ and $B$, respectively.   ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc298_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$\\-by-$N$ matrices $A$ and $B$ where each element is $0$ or $1$.  \nLet $A_{i,j}$ and $B_{i,j}$ denote the element at the $i$\\-th row and $j$\\-th column of $A$ and $B$, respectively.  \n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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