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 = [int(x) for i, x in enumerate(input().split())]
x = sorted(zip(x, range(1, n+1)))

stack = []
for v, i in x[::-1]:
    for _ in range(i-1):
        stack.append(i)

cur = 1
ans = []
res = []
cnt = [0]*(n+1)
for i in range(n):
    for _ in range(x[i][0]-cur):
        if stack:
            nxt = stack.pop()
        elif res:
            nxt = res.pop()
        else:
            print('No')
            exit()
        ans.append(nxt)
        cnt[nxt] += 1
    if cnt[x[i][1]] != x[i][1]-1:
        print('No')
        exit()
    ans.append(x[i][1])
    for _ in range(n-x[i][1]):
        res.append(x[i][1])
    cur = x[i][0]+1

ans += res

print('Yes')
print(*ans)