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 = tuple(map(int, input().split()))
XI = sorted((x, i+1) for i, x in enumerate(X))
L = [-1]*(n*n)
A = []
B = []
for x, i in XI:
  A = [i]*(i-1) + A
  B += [i]*(n-i)
  L[x-1] = i
now = 0
while A:
  if L[now] == -1:
    L[now] = A.pop()
  now += 1
now = n-1
while B:
  if L[now] == -1:
    L[now] = B.pop()
  now -= 1
C = [0]*(n+1)
for x, l in enumerate(L, 1):
  C[l] += 1
  if C[l] == l:
    if X[l-1] != x:
      print("No")
      exit()
print("Yes")
print(*L)