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 heapq import heappop,heappush

n = int(input())
a = list(map(int,input().split()))
dic = dict()
for i,ai in enumerate(a,1):
    if(ai-1 in dic):
        print('No')
        eixt()
    dic[ai-1] = i

hq = []
for i,ai in enumerate(a[1:],2):
    heappush(hq,(ai-i,i-1,i))

others = []
ans = []
for ind in range(n**2):
    if ind in dic:
        i = dic[ind]
        ans.append(i)
        others += [i] * (n-i)
        continue

    if(hq):
        num,rem,i = heappop(hq)
        if(num < ind):
            print('No')
            exit()
        elif(rem==1):
            ans.append(i)
        else:
            ans.append(i)
            heappush(hq,(num+1,rem-1,i))
    else:
        if(others):
            ans.append(others.pop())
        else:
            print('No')
            exit()



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