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:
def solve():
    N = int(input())
    Xs = [(X, i+1) for i, X in enumerate(map(int, input().split()))]

    N2 = N**2
    Xs.sort()

    As = [0] * (2*N2+1)
    for X, no in Xs:
        As[X] = no

    iA = 1
    for X, no in Xs:
        num = no-1
        while num:
            if As[iA] == 0:
                As[iA] = no
                num -= 1
            iA += 1
        if iA > X:
            return []

    for X, no in Xs:
        while As[iA] != 0:
            iA += 1
        if iA <= X:
            return []
        num = N-no
        while num:
            if As[iA] == 0:
                As[iA] = no
                num -= 1
            iA += 1

    if iA != N2+1:
        return []

    return As[1:iA]


anss = solve()
if anss:
    print('Yes')
    print(' '.join(map(str, anss)))
else:
    print('No')