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 solve():
    n=int(input())
    x=list(map(int,input().split()))
    list1=[]
    def ap1(num):
        list1.append(num)
    for i in range(n):
        ap1([x[i],i+1])
    str1= lambda val: val[0]
    list1.sort(key=str1)
    numa=[]
    numb=[]
    for i in range(n):
        num3=list1[i][1]
        numa+=[num3]*(num3-1)
        numb+=[num3]*(n-num3)
    count1=0
    count2=0
    count3=0
    ans=[]
    ansnum=0
    def countnum(num):
        return ans.count(num)
    def apans(num):
        ans.append(num)
    for i in range(n*n):
        yn=0
        if count1!=n:
            if i==list1[count1][0]-1:
                if countnum(list1[count1][1])!=list1[count1][1]-1:
                    ansnum=1
                    break
                apans(list1[count1][1])
                count1+=1
                yn=1
        if yn==0:
            if count2!=len(numa):
                apans(numa[count2])
                count2+=1
            elif count3!=len(numb):
                apans(numb[count3])
                count3+=1
            else:
                if i!=n*n-1:
                    ansnum=1
                    break
    if ansnum==1:
        print("No")
    else:
        print("Yes")
        print(*ans)
solve()