Problem:
Score : 500 points

Problem Statement

You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No.
If such a tuple exists, print Yes first, then print such subsets in the following format:

k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}

where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.

If there are multiple such tuples, any of them will be accepted.

Sample Input 1

3

Sample Output 1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.

Sample Input 2

4

Sample Output 2

No

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php

[$N] = fscanf(STDIN, "%d");
$target = -1;
for($i=1;$i<500;$i++){
    if($i * ($i+1) / 2 === $N){
        $target =$i;
        break;
    }elseif($i * ($i+1) / 2 > $N){
        break;
    }
}
if($target === -1){
    echo "No";
    exit;
}

echo "yes".PHP_EOL;
echo $target+1 .PHP_EOL;
$list = [];
$max = 1;
for($i=1;$i<=$target + 1; $i++){
    echo $target;
    for($j=1;$j<=$target;$j++){
        if(!isset($list[$j])){
            echo " ".$max;
            $list[$i][] = $max;
            $max++;
        }else{
            echo " ".$list[$j][count($list[$j])-1];
            unset($list[$j][count($list[$j])-1]);
        }
    }
    echo PHP_EOL;
}