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:
N = int(input())
X = list(map(int,input().split()))
Y = sorted([(x-1,i+1) for i,x in enumerate(X)])

ans = [None] * (N*N)
must = []
for i,n in Y:
    ans[i] = n
    must += [n]*(n-1)
must.reverse()

used = [0] * (N+1)
free = [1]
for i in range(N*N):
    if ans[i]:
        a = ans[i]
        if used[a] != a-1:
            print('No')
            exit()
        free += [a]*(N-a)
    elif must:
        a = must.pop()
        ans[i] = a
    else:
        if free:
            a = free.pop()
            ans[i] = a
        else:
            print('No')
            exit()
    used[ans[i]] += 1

for i in range(1,N+1):
    if used[i] != N:
        print('No')
        exit()

print('Yes')
print(*ans)