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:
def N(): return int(input())
def NM():return map(int,input().split())
def L():return list(NM())
def LN(n):return [N() for i in range(n)]
def LL(n):return [L() for i in range(n)]
n=N()
l=[(j,i) for i,j in enumerate(L(),1)]
l.sort()
ans=[0]*(n*n+1)
k=1
def No():
    print("No")
    quit()
for j,i in l:
    if ans[j]!=0:
        No()
    ans[j]=i
    x=0
    while x<i-1:
        if ans[k]==0:
            ans[k]=i
            x+=1
        k+=1
    if k>j:
        No()
l.sort(reverse=True)
k=n*n
for j,i in l:
    if i==n:
        continue
    x=0
    while x<n-i:
        if ans[k]==0:
            ans[k]=i
            x+=1
        k-=1
    if k<j:
        No()
print("Yes")
print(" ".join(map(str,ans[1:])))