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 PYTHON3):

Solution:
import sys
n = int(input())
x = list(map(int, input().split()))
s = sorted([[y-1, i+1] for i, y in enumerate(x)])
cur = 0
cnt = [0 for _ in range(n+1)]
fill_cur = 0
ans = []
residual = []
for i in range(n*n):
	if i == s[cur][0] and cnt[s[cur][1]] != s[cur][1]-1:
		print("No")
		sys.exit()
	elif i == s[cur][0]:
		ans.append(s[cur][1])
		cnt[s[cur][1]] += 1
		residual += [s[cur][1]] * (n - s[cur][1])
		cur += 1
		fill_cur = max(fill_cur, cur)
		if cur == n:
			break
	elif fill_cur < n:
		while cnt[s[fill_cur][1]] == s[fill_cur][1]-1:
			fill_cur += 1
			if fill_cur == n:
				if not residual:
					print("No")
					sys.exit()
				ans.append(residual.pop())
				break
		else:
			fill_cur = max(fill_cur, cur)
			ans.append(s[fill_cur][1])
			cnt[s[fill_cur][1]] += 1
	elif not residual:
		print("No")
		sys.exit()
	else:
		ans.append(residual.pop())
ans += residual
print("Yes")
print(*ans)