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, xxx):
    n2 = n ** 2
    yyy = sorted((x - 1, k) for k, x in enumerate(xxx, start=1))

    i = 0
    ans = [-1] * n2
    for x, k in yyy:
        j = k - 1
        while j:
            while ans[i] != -1:
                i += 1
            ans[i] = k
            i += 1
            j -= 1
        if i > x:
            return False
        ans[x] = k

    for x, k in yyy:
        while i < n2 and ans[i] != -1:
            i += 1
        if i < x:
            return False
        j = n - k
        while j:
            while i < n2 and ans[i] != -1:
                i += 1
            if i == n2:
                return False
            ans[i] = k
            i += 1
            j -= 1

    return ans


n = int(input())
xxx = list(map(int, input().split()))
result = solve(n, xxx)
if result:
    print('Yes')
    print(*result)
else:
    print('No')