Swap and Flip

AtCoder

IDkeyence2020_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ cards numbered $1, 2, ..., N$. Card $i$ ($1 \leq i \leq N$) has an integer $A_i$ written in red ink on one side and an integer $B_i$ written in blue ink on the other side. Initially, these cards are arranged from left to right in the order from Card $1$ to Card $N$, with the red numbers facing up. Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each $i$ ($1 \leq i \leq N - 1$), the integer facing up on the $(i+1)$\-th card from the left is not less than the integer facing up on the $i$\-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it. * Choose an integer $i$ ($1 \leq i \leq N - 1$). Swap the $i$\-th and $(i+1)$\-th cards from the left, then flip these two cards. ## Constraints * $1 \leq N \leq 18$ * $1 \leq A_i, B_i \leq 50$ ($1 \leq i \leq N$) * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ $B_1$ $B_2$ $...$ $B_N$ [samples]

Samples

Input #1

3
3 4 3
3 2 3

Output #1

1

By doing the operation once with $i = 1$, we have a sequence $[2, 3, 3]$ facing up, which is non-decreasing.

Input #2

2
2 1
1 2

Output #2

\-1

After any number of operations, we have the sequence $[2, 1]$ facing up, which is not non-decreasing.

Input #3

4
1 2 3 4
5 6 7 8

Output #3

0

No operation may be required.

Input #4

5
28 15 22 43 31
20 22 43 33 32

Output #4

\-1

Input #5

5
4 46 6 38 43
33 15 18 27 37

Output #5

API Response (JSON)

{
  "problem": {
    "name": "Swap and Flip",
    "description": {
      "content": "We have $N$ cards numbered $1, 2, ..., N$. Card $i$ ($1 \\leq i \\leq N$) has an integer $A_i$ written in red ink on one side and an integer $B_i$ written in blue ink on the other side. Initially, these",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "keyence2020_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ cards numbered $1, 2, ..., N$. Card $i$ ($1 \\leq i \\leq N$) has an integer $A_i$ written in red ink on one side and an integer $B_i$ written in blue ink on the other side. Initially, these...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments