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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
$n = intval(trim(fgets(STDIN)));
$size = getSize($n);
if($size === false){
    echo "No";
}else{
    $num = 1;
    for($i = 1; $i <= $size; $i++){
        for($j = 1; $j <= $size-$i+1; $j++){
            $map[$i][$j] = $num++;
        }
    }
    echo "Yes\n";
    echo $size + 1,"\n";
    for($i = 1; $i <= $size; $i++){
        echo $size," ";
        for($j = 1; $j <= $size; $j++){
            echo $map[min($i,$size+1-$j)][min($j, $size+1-$i)];
            echo " ";
        }
        echo "\n";
    }
    echo $size," ";
    for($i = 1; $i <= $size; $i++){
        echo $map[$i][$size+1-$i];
        if($i != $size)echo " ";
    }
    echo "\n";
}

function getSize($n){
    for($i = 2; $i < 10000; $i++){
        if($n == ($i*($i+1)/2)){
            return $i;
        }
    }
    return false;
}