Problem: 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.

Examples

Input

3
1 5 9


Output

Yes
1 1 1 2 2 2 3 3 3


Input

2
4 1


Output

No

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define F(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
int rd() {
	int f = 1; char c = getchar(); for (; !isdigit(c); c = getchar()) if (c == '-') f = -1;
	int x = 0; for (; isdigit(c); c = getchar()) x = x*10+c-'0'; return x*f;
}

const int N = 300000;

int n;
struct R {
	int i, x;
	friend int operator < (R a, R b) { return a.x < b.x; }
}r[N];
int a[N], m;

void run() { for (m++; a[m] > 0; m++); }

int main() {
	n = rd();
	F(i, 1, n) {
		int x = rd();
		r[i] = (R){i, x};
		a[x] = i;
	}
	sort(r+1, r+n+1);
	
	F(c, 1, n) {
		int i = r[c].i, x = r[c].x;
		F(j, 1, i-1)
			run(), a[m] = i;
		if (m > x) return puts("No"), 0;
	}
	
	run();
	F(c, 1, n) {
		int i = r[c].i, x = r[c].x;
		if (m < x) return puts("No"), 0;
		F(j, i+1, n)
			a[m] = i, run();
	}
	m--;
	
	puts("Yes");
	F(i, 1, m) printf("%d ", a[i]); puts("");
		
	return 0;
}