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)
x=[(x[i]-1,i+1) for i in range(N)]
x.sort()

for i in range(N):
    p,v=x[i]
    ans[p]=v

pos=0
for i in range(N):
    val,count=x[i]
    count-=1
    while count:
        while ans[pos]:
            pos+=1
        if pos>=val:
            print("No")
            exit()
        else:
            ans[pos]=x[i][1]
            count-=1


pos=N**2-1
for i in range(N-1,-1,-1):
    val,count=x[i]
    count-=1
    count=N-1-count
    while count:
        while ans[pos]:
            pos-=1
        if val>=pos:
            print("No")
            exit()
        else:
            ans[pos]=x[i][1]
            count-=1


print("Yes")
print(*ans)