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:
from collections import deque
from operator import itemgetter


n = int(input())
a = list(map(int, input().split()))

ans = [-1] * (n**2)
for i in range(n):
    ans[a[i] - 1] = i + 1

a_ind = [(j, a[j]) for j in range(n)]
a_ind = sorted(a_ind, key = itemgetter(1))
pos = 0
for j, _ in a_ind:
    k = j
    while True:
        if j == 0:
            break
        if ans[pos] != -1:
            pos += 1
        else:
            ans[pos] = k + 1
            pos += 1
            j -= 1

used = [False] * n
q = deque([])
cnt = [0] * n
for i in range(n**2):
    if ans[i] != -1:
        cnt[ans[i] - 1] += 1
        if cnt[ans[i] - 1] == ans[i]:
            for _ in range(n - ans[i]):
                q.append(ans[i])
            used[ans[i] - 1] = True
    else:
        if not q:
            print("No")
            exit()
        else:
            tmp = q.pop()
            ans[i] = tmp
      
cnt = [0] * n
for i in range(n**2):
    cnt[ans[i] - 1] += 1
    if cnt[ans[i] - 1] == ans[i]:
        if a[ans[i] - 1] != i + 1:
            print("No")
            exit()
print("Yes")
print(*ans)