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: Accepted)

use std::io;

fn main() {
    let mut str = String::new();
    
    let mut _bytes_read = io::stdin().read_line(&mut str)
        .expect("Failed to read line");
    
    let mut str2 = String::new();
    _bytes_read = io::stdin().read_line(&mut str2)
        .expect("Failed to read line");
    
    let parts: Vec<u32> = str2
        .trim()
        .split( ' ')
        .map(|s| s.parse().expect("Failed to parse"))
        .collect();
    
    if can_swap(parts) {
        print!("YES");
    } else {
        print!("NO");
    }
}

fn can_swap(objs: Vec<u32>) -> bool {
    let mut prev_prev = 0;
    let mut prev = objs[0];
    let mut mismatch_count: u32 = 0;
    let mut prev_lower_bound = 0;
    let mut to_swap = std::u32::MAX;
    for i in 1..(objs.len()) {
        let next = objs[i];
        if prev >= next {
            mismatch_count += 1;
            if mismatch_count > 2 || next <= prev_lower_bound || to_swap <= prev {
                return false;
            }
            
            prev_lower_bound = prev_prev;
            to_swap = prev;
        }
        prev_prev = prev;
        prev = next;
    }
    
    return mismatch_count != 1;
}