Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

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

<?php
  	fscanf(STDIN,"%d %d %d",$n,$m,$q);
	$abcd_li = array();
	for($i=0;$i<$q;$i++){
      $abcd_li[] = explode(" ",trim(fgets(STDIN)));
    }


  function getCpattern( $source, $m ){
   /* 引数 $source：選択元要素の配列 */
   /* 引数 $m：$source から異なる $m 個を選ぶ */

   $n = sizeof($source);

   return ptn( $source, $n, array(), 0, $n-$m+1 );

  }

  /* ptn：内部で再帰的に呼び出される関数 */
  function ptn( $source, $n, $subset, $begin, $end ){
   $p = array();
   for( $i = $begin; $i<$end; $i++){
    $tmp =array_merge( $subset, (array)$source[$i] );
    if( $end+1 <= $n ){
     $p = array_merge($p , ptn( $source, $n, $tmp, $i+1, $end+1 ) );
    }else{
     array_push( $p, $tmp );
    }
   }
   return $p;
  }



$source = array(); //元の要素を格納した配列
for($i=1;$i<=$m;$i++){
 	$source[] = "${i}"; 
}
$suretu_len = $n; // $source の中から重複なしで $m 個を選ぶ
//print_r($source);

$kumiawase = getCPattern( $source, $suretu_len ); //返ってくるのは全ての組み合わせを格納した配列

$sum=0;
$max_sum=0;

//print_r($kumiawase);
//echo count($kumiawase)."\n";

foreach($kumiawase as $suretu){
  foreach($abcd_li as $abcd){

  	if($suretu[$abcd[1]-1]-$suretu[$abcd[0]-1]==$abcd[2]){
   		$sum+=$abcd[3];
    }
  }
 
  $max_sum=max($sum,$max_sum);
  
  $sum=0;
}

echo $max_sum."\n";