Problem:
Score : 800 points

Problem Statement

You are given an integer sequence x of length N.
Determine if there exists an integer sequence a that satisfies all of the following conditions, and if it exists, construct an instance of a.

a is N^2 in length, containing N copies of each of the integers 1, 2, ..., N.

For each 1 ≤ i ≤ N, the i-th occurrence of the integer i from the left in a is the x_i-th element of a from the left.

Constraints

1 ≤ N ≤ 500

1 ≤ x_i ≤ N^2

All x_i are distinct.

Input

The input is given from Standard Input in the following format:

N
x_1 x_2 ... x_N

Output

If there does not exist an integer sequence a that satisfies all the conditions, print No.
If there does exist such an sequence a, print Yes in the first line, then print an instance of a in the second line, with spaces inbetween.

Sample Input 1

3
1 5 9

Sample Output 1

Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer 2 from the left in a in the output is the fifth element of a from the left.
Similarly, the condition is satisfied for the integers 1 and 3.

Sample Input 2

2
4 1

Sample Output 2

No

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

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

fn main() {
    let n: usize = read();
    let x: Vec<usize> = (0..n).map(|_| read::<usize>() - 1).collect();
    let mut data: Vec<(usize, usize)> = vec![(0, 0); n];
    for i in 0..n {
        data[i] = (x[i], i);
    }
    data.sort();

    let mut check = true;
    let inf = 1 << 29;
    let mut ans: Vec<usize> = vec![inf; n * n];
    for i in 0..n {
        ans[data[i].0] = i;
    }
    let mut now = 0;
    let mut count = 0;
    let mut before = true;
    for i in 0..n * n {
        if ans[i] == inf {
            if before {
                if data[now].1 == 0 {
                    now += 1;
                    count = 0;
                }
                ans[i] = data[now].1;
                count += 1;
                if count >= data[now].1 {
                    if now == n - 1 {
                        before = false;
                        now = 0;
                        count = data[now].1;
                    } else {
                        now += 1;
                        count = 0;
                    }
                }
            } else {
                if data[now].1 == n - 1 {
                    now += 1;
                    count = data[now].1;
                }
                ans[i] = data[now].1;
                count += 1;
                if i < n * n - 1 && count >= n - 1 {
                    now += 1;
                    count = data[now].1;
                }
            }
        } else {
            if (before && ((now < ans[i]) || (now == ans[i] && count < data[now].1)))
                || (!before && ((now > ans[i]) || (now == ans[i] && count > data[now].1)))
            {
                check = false;
                break;
            }
            ans[i] = data[ans[i]].1;
        }
    }

    if check {
        println!("Yes");
        for i in 0..n * n {
            if i != 0 {
                print!(" ");
            }
            print!("{}", ans[i] + 1);
        }
        println!();
    } else {
        println!("No");
    }
}

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")
}