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
N = int(input())
a = [-1]*N**2
x = list(map(lambda x:int(x)-1, input().split()))
x = list(zip(x, list(range(1, N+1))))
x.sort()
now = 0
for v, i in x:
    if a[v]>=0:
        print('No')
        sys.exit()
    a[v] = i
    cnt = 0
    while cnt < i-1:
        if now==v:
            print('No')
            sys.exit()
        if a[now]<0:
            a[now] = i
            cnt+=1
        now+=1
now = N*N-1
for v, i in reversed(x):
    cnt = 0
    while cnt<N-i:
        if now<=v:
            print('No')
            sys.exit()
        if a[now]<0:
            a[now] = i
            cnt+=1
        now-=1
if all(v >= 0 for v in a):
    print('Yes')
    print(*a)
else:
    print('No')