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
readline = sys.stdin.readline

def check(A, X):
    N = len(A)
    Ans = [None]*(N**2)
    cnt = 0
    po = 0
    for i in range(N):
        a, x = A[i], X[i]
        a += 1
        x -= 1
        if Ans[x] is not None:
            return False
        cnt += a-1
        if cnt > x:
            return False
        cnt += 1
        Ans[x] = a
        res = a-1
        while res:
            if Ans[po] is None:
                res -= 1
                Ans[po] = a
            po += 1
    
    cnt = 0
    po = N**2-1
    for i in range(N-1, -1, -1):
        a, x = A[i], X[i]
        a += 1
        x -= 1
        cnt += N-a
        if N**2-x < 1 + cnt:
            return False
        cnt += 1
        res = N-a
        while res:
            if Ans[po] is None:
                res -= 1
                Ans[po] = a
            po -= 1
    
    return Ans
N = int(readline())
X = list(map(int, readline().split()))
A = sorted(list(range(N)), key = lambda x: X[x])
X.sort()

Ans = check(A, X)
if Ans:
    print('Yes')
    print(*Ans)
else:
    print('No')