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 = list(map(int, input().split()))
ans = [0] * (n**2+1)
for k,v in enumerate(x):
  ans[v] = k+1
x = sorted([[v,k] for k,v in enumerate(x)])
now = 1
for k,v in x:
  num = v + 1
  while v:
    if ans[now]:
      if ans[now] == num:
        print("No")
        exit()
    else:
      ans[now] = num
      v -= 1
    now += 1
now2 = n ** 2
for k,v in reversed(x):
  num = v + 1
  quant = n - num
  while quant:
    if ans[now2]:
      if ans[now2] == num:
        print("No")
        exit()
    else:
      ans[now2] = num
      quant -= 1
    now2 -= 1
print("Yes")
print(*ans[1:])