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);
	$abcd = array();
	for($i=0;$i<$q;$i++){
  		$abcd[] = explode(" ",trim(fgets(STDIN)));
    }
function dfs(&$all_pattern,$array,$n,$m){
   if(count($array)==$n){
        $all_pattern[] = $array;
        return;//こっちのリターンは上の階層にいかない
      }
  	 (count($array)!=0) ? $prev_last=end($array):$prev_last=0;
      for($i=$prev_last;$i<=$m;$i++){
        $array[] = $i;
        dfs($all_pattern,$array,$n,$m);
        array_pop($array);
      }
      return;//こっちのリターンは上の階層にいく
}
  $all_pattern=array();

dfs($all_pattern,[],$n,$m);
//print_r($all_pattern);

$max=0;
$sum=0;

foreach($all_pattern as $pattern){
  foreach($abcd as $a){
  	if($pattern[$a[1]-1]-$pattern[$a[0]-1]==$a[2]){
    	$sum+=$a[3];
  	}
  }
  $max=max($max,$sum);
  $sum=0;
}

echo $max."\n";