Simultaneous Swap

AtCoder

IDabc296_f

Time2000ms

Memory256MB

Difficulty—

You are given two sequences of $N$ numbers: $A=(A_1,A_2,\ldots,A_N)$ and $B=(B_1,B_2,\ldots,B_N)$. Takahashi can repeat the following operation any number of times (possibly zero). > Choose three pairwise distinct integers $i$, $j$, and $k$ between $1$ and $N$. > Swap the $i$\-th and $j$\-th elements of $A$, and swap the $i$\-th and $k$\-th elements of $B$. If there is a way for Takahashi to repeat the operation to make $A$ and $B$ equal, print `Yes`; otherwise, print `No`. Here, $A$ and $B$ are said to be equal when, for every $1\leq i\leq N$, the $i$\-th element of $A$ and that of $B$ are equal. ## Constraints * $3 \leq N \leq 2\times 10^5$ * $1\leq A_i,B_i\leq N$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_N$ [samples]

Samples

Input #1

3
1 2 1
1 1 2

Output #1

Yes

Performing the operation once with $(i,j,k)=(1,2,3)$ swaps $A_1$ and $A_2$, and swaps $B_1$ and $B_3$,  
making both $A$ and $B$ equal to $(2,1,1)$. Thus, you should print `Yes`.

Input #2

3
1 2 2
1 1 2

Output #2

No

There is no way to perform the operation to make $A$ and $B$ equal, so you should print `No`.

Input #3

5
1 2 3 2 1
3 2 2 1 1

Output #3

Yes

Input #4

8
1 2 3 4 5 6 7 8
7 8 5 6 4 3 1 2

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "Simultaneous Swap",
    "description": {
      "content": "You are given two sequences of $N$ numbers: $A=(A_1,A_2,\\ldots,A_N)$ and $B=(B_1,B_2,\\ldots,B_N)$. Takahashi can repeat the following operation any number of times (possibly zero). > Choose three pai",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc296_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given two sequences of $N$ numbers: $A=(A_1,A_2,\\ldots,A_N)$ and $B=(B_1,B_2,\\ldots,B_N)$.\nTakahashi can repeat the following operation any number of times (possibly zero).\n\n> Choose three pai...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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