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
sys.setrecursionlimit(10000000)
MOD = 10 ** 9 + 7
INF = 10 ** 15

def main():
    N = int(input())
    X = list(enumerate(map(int,input().split())))
    X.sort(key = lambda x:x[1])
    
    M = N*N
    ans = [None] * M
    now = 0
    for i,x in X:
        ans[x - 1] = i + 1
        count = i
        while count > 0:
            while ans[now]:
                now += 1
            if now >= x:
                print('No')
                return
            ans[now] = i + 1
            count -= 1
    
    now = M - 1
    for i,x in X[::-1]:
        count = N - i - 1
        while count > 0:
            while ans[now]:
                now -= 1
            if now < x:
                print('No')
                return
            ans[now] = i + 1
            count -= 1
    print('Yes')
    print(' '.join(map(str,ans)))
if __name__ == '__main__':
    main()