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()))

x_ = [(x[i], i+1) for i in range(N)]
x_.sort(key=lambda s: s[0])
seq = [x_[i][1] for i in range(N)]
left = []
for s in seq:
    left.extend([s] * (s-1))
right = []
for s in reversed(seq):
    right.extend([s] * (N - s))
right.reverse()
ans_raw = left + right
ans_raw.reverse()

ans = [0] * (N**2)
for i, xi in enumerate(x):
    ans[xi-1] = -(i+1)
for i in range(N**2):
    if ans[i] == 0:
        ans[i] = ans_raw.pop()

cnt_list = [0] * (N+1)
for i in range(N**2):
    if ans[i] < 0:
        if cnt_list[-ans[i]] != -ans[i]-1:
            print('No')
            exit()
    else:
        cnt_list[ans[i]] += 1

print('Yes')
ans = list(map(abs, ans))
print(*ans)