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 collections import defaultdict
n = int(input())
x = list(map(int,input().split()))
for i in range(n):
  if x[i]-1 < i or x[i]-1 > n*n-n+i:
    print("No")
    exit()
    
ans = [-1]*n*n
for i in range(n):
  ans[x[i]-1] = i+1
x2 = []
for i in range(n):
  x2.append((x[i],i+1))
x2.sort()
yusen = deque([])
ato = deque([])
for i in range(n):
  yusen.extend([x2[i][1]]*(x2[i][1]-1))
  ato.extend([x2[i][1]]*(n-x2[i][1]))
for i in range(n*n):
  if ans[i] == -1:
    if yusen:
      ko = yusen.popleft()
      ans[i] = ko
    else:
      ko = ato.popleft()
      ans[i] = ko
d = defaultdict(int)
for i in range(n*n):
  d[ans[i]] += 1
  if d[ans[i]] == ans[i]:
    if i+1 != x[ans[i]-1]:
      print("No")
      exit()
print("Yes")
print(*ans)