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: Accepted)

use std::collections::VecDeque;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: usize = sc.read();
    let x: Vec<usize> = sc.vec(n);
    let mut x: Vec<(usize, usize)> = x
        .into_iter()
        .enumerate()
        .map(|(i, pos)| (i + 1, pos - 1))
        .collect();
    x.sort_by_key(|x| x.1);
    let mut ans = vec![0; n * n];
    let mut cur = 0;
    let mut q = VecDeque::new();
    for &(i, pos) in x.iter() {
        while cur < pos {
            if ans[cur] == 0 {
                q.push_back(cur);
            }
            cur += 1;
        }
        for _ in 0..(i - 1) {
            if let Some(ans_i) = q.pop_front() {
                assert_eq!(ans[ans_i], 0);
                ans[ans_i] = i;
            } else {
                println!("No");
                return;
            }
        }
        assert_eq!(cur, pos);
        ans[cur] = i;
        cur += 1;
    }

    let mut k_th_k = vec![false; n * n];
    for &(_, pos) in x.iter() {
        k_th_k[pos] = true;
    }

    let mut q = VecDeque::new();
    for i in (0..(n * n)).rev() {
        if k_th_k[i] {
            assert_ne!(ans[i], 0);
            let v = ans[i];
            let remain = n - v;
            for _ in 0..remain {
                if let Some(i) = q.pop_front() {
                    assert_eq!(ans[i], 0);
                    ans[i] = v;
                } else {
                    println!("No");
                    return;
                }
            }
        } else if ans[i] == 0 {
            q.push_front(i);
        }
    }

    println!("Yes");
    for i in 0..(n * n) {
        if i > 0 {
            print!(" ");
        }
        print!("{}", ans[i]);
    }
    println!();
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}