Problem:
Score : 200 points

Problem Statement

We have a sequence p = {p_1,\ p_2,\ ...,\ p_N} which is a permutation of {1,\ 2,\ ...,\ N}.

You can perform the following operation at most once: choose integers i and j (1 \leq i < j \leq N), and swap p_i and p_j. Note that you can also choose not to perform it.

Print YES if you can sort p in ascending order in this way, and NO otherwise.

Constraints

All values in input are integers.

2 \leq N \leq 50

p is a permutation of {1,\ 2,\ ...,\ N}.

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print YES if you can sort p in ascending order in the way stated in the problem statement, and NO otherwise.

Sample Input 1

5
5 2 3 4 1

Sample Output 1

YES

You can sort p in ascending order by swapping p_1 and p_5.

Sample Input 2

5
2 4 3 5 1

Sample Output 2

NO

In this case, swapping any two elements does not sort p in ascending order.

Sample Input 3

7
1 2 3 4 5 6 7

Sample Output 3

YES

p is already sorted in ascending order, so no operation is needed.

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
  let stdin = stdin();
  let stdin = stdin.lock();
  let token: String = stdin
    .bytes()
    .map(|c| c.expect("failed to read char") as char)
    .skip_while(|c| c.is_whitespace())
    .take_while(|c| !c.is_whitespace())
    .collect();
  token.parse().ok().expect("failed to parse token")
}

fn read_n<T: FromStr>(n: usize) -> Vec<T> {
  read_n_logic::<T>(n, vec![])
}

fn read_n_logic<T: FromStr>(n: usize, mut a: Vec<T>) -> Vec<T> {
  match n {
    0 => a,
    _ => {
      a.push(read::<T>());
      read_n_logic(n - 1, a)
    }
  }
}

fn main() {
  let n = read::<usize>();
  let p = read_n::<usize>(n);
  let mut last_num = 0;
  let mut index = 0;
  let mut segment: Vec<usize> = vec![0];

  for pi in p {
    if last_num > pi {
      if last_num != 0 {
        index += 1;
      }
      if index == segment.len() {
        segment.push(0)
      }
    }
    segment[index] += 1;
    if index > 2 {
      return println!("NO");
    }
    last_num = pi;
  }

  let mut counter = 0;
  for segment_len in segment {
    if segment_len >= 2 {
      counter += 1;
      if counter >= 2 {
        return println!("NO");
      }
    }
  }

  println!("YES")
}