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)

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 mut x = vec![];
    for i in 0..n {
        let a: usize = sc.read();
        x.push((a, i));
    }
    x.sort();

    let mut ans = vec![None; n * n];
    let mut hole_head = 0;
    let mut cur_sum = 0;
    for &(x, i) in x.iter() {
        let lower_count = i + 1;
        if cur_sum + lower_count > x {
            println!("No");
            return;
        }
        cur_sum += lower_count;
        ans[x - 1] = Some(i + 1);
        for _ in 1..lower_count {
            while ans[hole_head].is_some() {
                hole_head += 1;
                if hole_head >= n * n {
                    println!("No");
                    return;
                }
            }
            ans[hole_head] = Some(i + 1);
            hole_head += 1;
        }
    }

    let mut hole_tail = n * n - 1;
    let mut cur_sum = 0;
    for &(x, i) in x.iter().rev() {
        let upper_count = n - (i + 1);
        if cur_sum + upper_count > n * n - x {
            println!("No");
            return;
        }
        cur_sum += upper_count;
        for _ in 0..upper_count {
            while ans[hole_tail].is_some() {
                if hole_tail == 0 {
                    println!("No");
                    return;
                }
                hole_tail -= 1;
            }
            if hole_tail <= x - 1 {
                println!("No");
                return;
            }
            ans[hole_tail] = Some(i + 1);
        }
    }

    println!("Yes");
    for ans in ans.into_iter() {
        print!("{} ", ans.unwrap());
    }
    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) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.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()
    }
}