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
n = int(input())
x = list(map(int,input().split()))
y = [(x[i],i+1) for i in range(n)]
y.sort()
rng = [(y[0][1],(n-1)*n//2+1)]
bef = deque([y[0][1]]*(y[0][1]-1))
for i in range(1,n):
  a,b = rng[-1]
  rng.append((a+y[i][1],b+n-y[i-1][1]+1))
  bef.extend([y[i][1]]*(y[i][1]-1))
ans = []
cnt = 0
for i in range(n):
  goal = y[i][0]
  if cnt>goal or not rng[i][0] <= y[i][0] <= rng[i][1]:
    print("No")
    exit()
  while cnt+1<goal:
    if not bef:
      print("No")
      exit()
    ans.append(bef.popleft())
    cnt += 1
  ans.append(y[i][1])
  cnt += 1
  bef.extend([y[i][1]]*(n-y[i][1]))
while bef:
  ans.append(bef.popleft())
print("Yes")
print(*ans,sep=" ")