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
xs = gets.split.map(&:to_i)
reqs = []
N.times do |i|
    reqs[i] = [i+1, xs[i]]
end

reqs.sort_by!{|arr|arr[1]}

before_queue = []
after_queue = []
reqs.each do |i, x|
    before_queue.concat(Array.new(i - 1, i))
    after_queue.concat(Array.new(N - i, i))
end
queue = before_queue + after_queue
count = Array.new(N+1, 0)

ans = []
(1..N*N).each do |n|
    if reqs.length > 0 && reqs[0][1] == n
        i, x = reqs.shift
        ans.push(i)
        count[i] += 1
        if count[i] != i
            puts 'No'
            exit
        end
    else
        i = queue.shift
        ans.push(i)
        count[i] += 1
    end
end

puts 'Yes'
puts ans.join(' ')