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)

fn read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim_right().to_owned()
}

fn comb2(n: usize) -> Vec<(usize, usize)> {
    let mut v = Vec::new();
    for i in 0..(n - 1) {
        for j in (i + 1)..n {
            v.push((i, j));
        }
    }
    v
}

trait Sortable {
    fn is_sorted(&self) -> bool;
}

impl Sortable for Vec<u32> {
    fn is_sorted(&self) -> bool {
        (*self).windows(2).all(|w| w[0] <= w[1])
    }
}

fn main() {
    read_line();
    let nums: Vec<u32> = read_line().split_whitespace().map(|x| x.parse().unwrap()).collect();
    
    if nums.is_sorted() {
        println!("YES");
        return;
    }

    let sortable = comb2(nums.len())
        .into_iter()
        .any(|(i, j)| {
            let mut v = nums.clone();
            v.swap(i, j);
            v.is_sorted()
        });

    println!("{}", if sortable { "YES" } else { "NO" });
}