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:
#d greedy might work well
n = int(input())
a = [int(i) for i in input().split()]

#make the pairs of place index and its value
a_num = [(v,num+1) for num,v in enumerate(a)]

ans = [0] * (n**2)
for i,v in enumerate(a):
    ans[v-1] = i+1

a_num.sort()

judge = True

ind = 0
for v,num in a_num:
    # we do not use the value v in this loop
    cnt = 0
    while not (cnt==num-1):
        if ans[ind]==0: #not yet written
            ans[ind]=num
            cnt += 1
        elif ans[ind]==num: #impossible to make an array
            judge = False
            break
        ind += 1

        
a_num.reverse()
ind = n*n-1
for v,num in a_num:
    # we do not use the value v in this loop
    cnt = 0
    while not (cnt==n-num):
        if ans[ind]==0: #not yet written
            ans[ind]=num
            cnt += 1
        elif ans[ind]==num: #impossible to make an array
            judge = False
            break
        ind -= 1

if judge==True:
    print("Yes")
    print(*ans)
else:
    print("No")