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:
import sys
input = sys.stdin.readline
N = int(input())
a = list(map(int, input().split()))
b = [(a[i], i) for i in range(N)]
b.sort()
res = [0] * pow(N, 2)
for i in range(N): res[a[i] - 1] = i + 1
#print(res, b)
for k in range(N):
  i = b[k][1]
  x = i
  if i == 0: continue
  for j in range(a[i] - 1):
    if res[j]: continue
    res[j] = i + 1
    x -= 1
    if x == 0: break
  #print(res, i, a[i])
  if x:
    print("No")
    exit(0)
  #print(res)
#print(res)
for i in range(N):
  x = N - i - 1
  for j in range(a[i], N ** 2):
    if res[j]: continue
    res[j] = i + 1
    x -= 1
    if x == 0: break
  #print(res)
  if x:
    print("No")
    exit(0)
print("Yes")
print(*res)