Two Permutations

AtCoder

IDagc038_f

Time8000ms

Memory256MB

Difficulty—

Snuke has permutations $(P_0,P_1,\cdots,P_{N-1})$ and $(Q_0,Q_1,\cdots,Q_{N-1})$ of $(0,1,\cdots,N-1)$. Now, he will make new permutations $A$ and $B$ of $(0,1,\cdots,N-1)$, under the following conditions: * For each $i$ ($0 \leq i \leq N-1$), $A_i$ should be $i$ or $P_i$. * For each $i$ ($0 \leq i \leq N-1$), $B_i$ should be $i$ or $Q_i$. Let us define the distance of permutations $A$ and $B$ as the number of indices $i$ such that $A_i \neq B_i$. Find the maximum possible distance of $A$ and $B$. ## Constraints * $1 \leq N \leq 100000$ * $0 \leq P_i \leq N-1$ * $P_0,P_1,\cdots,P_{N-1}$ are all different. * $0 \leq Q_i \leq N-1$ * $Q_0,Q_1,\cdots,Q_{N-1}$ are all different. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $P_0$ $P_1$ $\cdots$ $P_{N-1}$ $Q_0$ $Q_1$ $\cdots$ $Q_{N-1}$ [samples]

Samples

Input #1

4
2 1 3 0
0 2 3 1

Output #1

3

For example, if we make $A=(0,1,2,3)$ and $B=(0,2,3,1)$, the distance will be $3$, which is the maximum result possible.

Input #2

10
0 4 5 3 7 8 2 1 9 6
3 8 5 6 4 0 2 1 7 9

Output #2

Input #3

32
22 31 30 29 7 17 16 3 14 9 19 11 2 5 10 1 25 18 15 24 20 0 12 21 27 4 26 28 8 6 23 13
22 3 2 7 17 9 16 4 14 8 19 26 28 5 10 1 25 18 15 13 11 0 12 23 21 20 29 24 27 6 30 31

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Two Permutations",
    "description": {
      "content": "Snuke has permutations $(P_0,P_1,\\cdots,P_{N-1})$ and $(Q_0,Q_1,\\cdots,Q_{N-1})$ of $(0,1,\\cdots,N-1)$. Now, he will make new permutations $A$ and $B$ of $(0,1,\\cdots,N-1)$, under the following condit",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 8000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc038_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has permutations $(P_0,P_1,\\cdots,P_{N-1})$ and $(Q_0,Q_1,\\cdots,Q_{N-1})$ of $(0,1,\\cdots,N-1)$.\nNow, he will make new permutations $A$ and $B$ of $(0,1,\\cdots,N-1)$, under the following condit...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments