Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

3
1 5 9

Sample Output 1

Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer 2 from the left in a in the output is the fifth element of a from the left.
Similarly, the condition is satisfied for the integers 1 and 3.

Sample Input 2

2
4 1

Sample Output 2

No

Solution in Ruby (2.3.3) (judge verdict: Accepted)

N,*A=`dd`.split.map &:to_i;r={};B=[*1..N].sort_by{|i|r[A[i-1]-1]=i;A[i-1]};s=Hash.new 0;z=[];N.times{|i|n=B[N-i-1];z=[n]*~-n+z+[B[i]]*(N-B[i])};puts (N*N).times.any?{|i|z<<x=r[i]||z.shift;s[x]+=1;r[i]&&x!=s[x]}?:No:[:Yes,z]