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: Wrong Answer)

n=gets.to_i
a=gets.split.map{|i|i.to_i-1}
m=[]*n**2
n.times do |i|
  m[a[i]]=i
end
n.times do |i|
  a[i]=[a[i],i]
end
a=a.sort{|x,y|x[0]<=>y[0]}
pi=0
pm=n**2-1
n.times do |i|
  c=a[i][1]
  while c!=0
    if m[pi]
      pi+=1
    else
      m[pi]=a[i][1]
      c-=1
    end
    break if pi==n**2
    break if pi>=a[i][0]
  end
  c=n-a[i][1]-1
  while c!=0
    if m[pm]
      pm-=1
    else
      m[pm]=a[i][1]
      c-=1
    end
    break if pm==-1
  end
  break if pm==-1
  break if pm<=a[i][0]
end
if m.include?(nil)
  puts :No
else
  puts :Yes
  puts m.map{|i|i+1}.*" "
end