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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
    $n = trim(fgets(STDIN));
	$x = explode(" ", trim(fgets(STDIN)));
	$n2 = $n*$n;
	for($i=1; $i<=$n2; $i++){
	    $a[$i] = 0;
	    $b[$i] = 0;
	}
	for($i=1; $i<=$n; $i++){
	    $a[$x[$i-1]] = $i;
	}
	
	$f = true;
	$m = 0;
	$c = 1;
	for($i=1; $i<=$n2; $i++){
	    if($f && $a[$i] != 0){
	        $m = $a[$i];
	        for($j=1; $j<$m; $j++){
	            while($a[$c] != 0 || $b[$c] != 0){
	                $c++;
	                if($c>$n2){
	                    $f = false;
	                    break;
	                }
	            }
	            if(!$f) break;
	            $b[$c] = $m;
	        }
	        if($c>$i) $f = false;
	    }
	}
	
	$c = $n2;
	for($i=$n2; $i>0; $i--){
	    if($f && $a[$i] != 0){
	        $m = $a[$i];
	        for($j=$m; $j<$n; $j++){
	            while($a[$c] != 0 || $b[$c] != 0){
	                $c--;
	                if($c<1){
	                    $f = false;
	                    break;
	                }
	            }
	            if(!$f) break;
	            $b[$c] = $m;
	        }
	        if($c<$i) $f = false;
	    }
	}
	if($f){
	    echo "Yes"."\n";
	    for($i=1; $i<=$n2; $i++){
    	    if($a[$i] != 0) $ans = $a[$i];
    	    else $ans = $b[$i];
    	    echo $ans." ";
	    }
	} else echo "No";
?>