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
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

N = int(input())
X = sorted((x,i) for i,x in enumerate((int(x) for x in input().split()),1))

arr = []
for x,i in X:
    arr += [i] * (i-1)
for x,i in X:
    arr += [i] * (N-i)

x_to_i = dict(X)

arr = arr[::-1]
answer = []
counter = [0] * (N+1)
bl = True
for x in range(1,N*N+1):
    if x in x_to_i:
        i = x_to_i[x]
        counter[i] += 1
        bl &= (counter[i] == i)
    else:
        i = arr.pop()
        counter[i] += 1
    answer.append(i)

if bl:
    print('Yes')
    print(*answer)
else:
    print('No')