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:
from heapq import heappush, heappop
import sys
input = sys.stdin.readline

N = int(input())
x = [0] + list(map(int, input().split()))
v = []
heap = []
a = [-1] * (N * N + 1)
for i in range(1, N+1):
    a[x[i]] = i
    for j in range(1, i):
        v.append((x[i] - j, i))
v.sort(reverse=True)
for i in range(1, N * N + 1):
    if a[i] != -1:
        n = a[i]
        for j in range(N - n):
            heappush(heap, (N * N - j, n))
        continue
    if v:
        j, k = v.pop()
        if x[k] < i:
            print('No')
            exit()
        a[i] = k
    else:
        if not heap:
            print('No')
            exit()
        j, k = heappop(heap)
        a[i] = k
print('Yes')
print(*a[1:])