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:
import collections
n = int(input())
x = list(map(int, input().split()))
x = list(enumerate(x, 1))
x.sort(key = lambda x: x[1])
li = []
dic = {j: i for i, j in x}
for i, j in x:
    li += [i] * (i - 1)
for i, j in x:
    li += [i] * (n - i)
li = collections.deque(li)
ans = []
cnt = [0 for i in range(n + 1)]
for i in range(1, n ** 2 + 1):
    if i in dic:
        m = dic[i]
        if cnt[m] != m - 1:
            print("No")
            exit()
    else:
        m = li.popleft()
    cnt[m] += 1
    ans.append(m)
print("Yes")
print(*ans)