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
import sys

N = int(input())

x = list(map(int,input().split()))

mustuse = deque([])
ableuse = deque([])

xlis = []
ans = [None] * (N ** 2)

for i in range(N):
    ans[x[i]-1] = i+1
    xlis.append([x[i],i+1])

xlis.sort()

for i in range(N):

    for j in range(xlis[i][1]-1):
        mustuse.append(xlis[i][1])

#print (ans)
#print (mustuse)

for i in range(N**2):

    if ans[i] != None:

        if len(mustuse) > 0 and mustuse[0] == ans[i]:
            print ("No")
            sys.exit()
        for j in range(N-ans[i]):
            ableuse.append(ans[i])

    else:

        if len(mustuse) > 0:
            ans[i] = mustuse.popleft()

        elif len(ableuse) > 0:
            ans[i] = ableuse.popleft()

        else:
            print ("No")
            sys.exit()

print ("Yes")
print (" ".join(map(str,ans)))