Equals

AtCoder

IDarc097_b

Time2000ms

Memory256MB

Difficulty—

We have a permutation of the integers from $1$ through $N$, $p_1$, $p_2$, .., $p_N$. We also have $M$ pairs of two integers between $1$ and $N$ (inclusive), represented as $(x_1,y_1)$, $(x_2,y_2)$, .., $(x_M,y_M)$. AtCoDeer the deer is going to perform the following operation on $p$ as many times as desired so that the number of $i$ ($1$ $≤$ $i$ $≤$ $N$) such that $p_i = i$ is maximized: * Choose $j$ such that $1$ $≤$ $j$ $≤$ $M$, and swap $p_{x_j}$ and $p_{y_j}$. Find the maximum possible number of $i$ such that $p_i = i$ after operations. ## Constraints * $2$ $≤$ $N$ $≤$ $10^5$ * $1$ $≤$ $M$ $≤$ $10^5$ * $p$ is a permutation of integers from $1$ through $N$. * $1$ $≤$ $x_j,y_j$ $≤$ $N$ * $x_j$ $≠$ $y_j$ * If $i$ $≠$ $j$, ${x_i,y_i}$ $≠$ ${x_j,y_j}$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $p_1$ $p_2$ $..$ $p_N$ $x_1$ $y_1$ $x_2$ $y_2$ $:$ $x_M$ $y_M$ [samples]

Samples

Input #1

Output #1

2

If we perform the operation by choosing $j=1$, $p$ becomes `1 3 5 4 2`, which is optimal, so the answer is $2$.

Input #2

Output #2

3

If we perform the operation by, for example, choosing $j=1$, $j=2$, $j=1$ in this order, $p$ becomes `1 2 3`, which is obviously optimal. Note that we may choose the same $j$ any number of times.

Input #3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Output #3

Input #4

5 1
1 2 3 4 5
1 5

Output #4

5

We do not have to perform the operation.

API Response (JSON)

{
  "problem": {
    "name": "Equals",
    "description": {
      "content": "We have a permutation of the integers from $1$ through $N$, $p_1$, $p_2$, .., $p_N$. We also have $M$ pairs of two integers between $1$ and $N$ (inclusive), represented as $(x_1,y_1)$, $(x_2,y_2)$, ..",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc097_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a permutation of the integers from $1$ through $N$, $p_1$, $p_2$, .., $p_N$. We also have $M$ pairs of two integers between $1$ and $N$ (inclusive), represented as $(x_1,y_1)$, $(x_2,y_2)$, .....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments