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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;

#define mp make_pair
#define ff first
#define ss second
#define pb push_back
#define pf push_front
#define popb pop_back
#define popf pop_front
#define all(v) v.begin(),v.end()

const int maxn = 5e5 + 100;
const ll inf = 2e18, mod = 1e9 + 7;

int n, x[maxn], a[maxn];
bool alpha[maxn], valid = true;

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(0);

	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> x[i], x[i]--;

	for (int i = 0; i < n; i++)
	{
		if (a[x[i]])
			valid = false;
		a[x[i]] = i + 1;
		alpha[x[i]] = true;
	}
	int pos = 0;
	for (int i = 0; i < n * n; i++)
	{
		if (a[i])
		{
			int cnt = a[i] - 1;
			while (cnt && pos <= i)
			{
				if (a[pos])
					pos++;
				else
					a[pos] = a[i], cnt--, pos++;
			}
			if (cnt)
				valid = false;
		}
	}

	pos = n * n - 1;
	for (int i = n * n - 1; i >= 0; i--)
	{
		if (alpha[i])
		{
			int cnt = n - a[i];
			while (cnt && pos >= i)
			{
				if (a[pos])
					pos--;
				else
					a[pos] = a[i], cnt--, pos--;
			}
			if (cnt)
				valid = false;
		}
	}

	if (valid)
	{
		cout << "Yes" << endl;
		for (int i = 0; i < n * n; i++)
			cout << a[i] << ' ';
		cout << endl;
	}
	else
		cout << "No" << endl;
}