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 = gets.to_i
x = gets.split.map{|i|[i.to_i,0]}
a = []
b = []
n.times do |i|
    x[i][1] = i+1
end
x.sort!
n.times do |i|
    (x[i][1]-1).times do
        a << x[i][1]
    end
end
ans = []
j = 0
(n*n).times do |i|
    if j < n && x[j][0] == i+1
        if (a.include?(x[j][1]))
            puts "No"
            exit
        end
        ans << x[j][1]
        (n-x[j][1]).times do
            b << x[j][1]
        end
        j += 1
    else
        if !a.empty?
            ans << a.shift
        elsif !b.empty?
            ans << b.pop
        else
            puts "No"
            exit
        end
    end
end
puts "Yes",ans.join(" ")