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:
N=int(input())
X=[]
for i,x in enumerate(input().split()):
  X.append((int(x)-1,i+1))
X.sort()
a,b,c,k,l=0,0,0,0,0
ans=[]
for i in range(N*N):
  if b<=N-1:
    x,p=X[b]
    if x==i:
      if a<=b and p!=1:
        print("No")
        exit()
      ans.append(p)
      b+=1
      continue
  if a<=N-1:
    y,q=X[a]
    if q==1:
      a+=1
      if a==N:
        z,r=X[c]
        if c>=b:
          print("No")
          exit()
        if r==N:
          c+=1
          l=0
          z,r=X[c]
        ans.append(r)
        l+=1
        if l==N-r:
          c+=1
          l=0
        continue
      else:
        y,q=X[a]
        k=0
    ans.append(q)
    k+=1
    if k==q-1:
      a+=1
      k=0
  else:
    z,r=X[c]
    if c>=b:
      print("No")
      exit()
    if r==N:
      c+=1
      l=0
      z,r=X[c]
    ans.append(r)
    l+=1
    if l==N-r:
      c+=1
      l=0
  
print("Yes")
print(" ".join(map(str,ans)))