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 PYTHON):

Solution:
n=int(raw_input())
x=map(int,raw_input().split())
ans=[-1]*(n**2+1)
for i in xrange(n):
    if ans[x[i]]!=-1:
        print("No")
        exit()
    ans[x[i]]=i+1
for i in xrange(1,n**2+1):
    if ans[i]!=-1:
        cnt=ans[i]-1
        for j in xrange(1,i):
            if cnt==0:break
            if ans[j]==-1:
                cnt-=1
                ans[j]=ans[i]
        if cnt>0:
            print("No")
            exit()

check=[False]*(n+1)
for i in xrange(n**2,0,-1):
    if ans[i]!=-1 and (not check[ans[i]]):
        cnt=n-ans[i]
        check[ans[i]]=True
        for j in xrange(n**2,i,-1):
            if cnt==0:break
            if ans[j]==-1:
                cnt-=1
                ans[j]=ans[i]
        if cnt>0:
            print("No")
            exit()
print("Yes")
print(" ".join(map(str,ans[1:])))