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: Accepted)

<?php
fscanf(STDIN, '%d %d %d', $length, $max, $quad);
$map = [];
$highScore = 0;
for ($i=0; $i < $quad; $i++) { 
    $nums = array_map('intval', explode(' ', trim(fgets(STDIN))));
    $map[] = $nums;
}
$arr = [1];
dfs($arr);
echo $highScore;

function dfs($arr) {
    global $length, $max, $highScore;
    $size = count($arr);
    if ($size-1 == $length) {
        $highScore = setHighScore($arr);
        return $highScore;
    }
    $arr[] = $arr[$size-1];
    $size++;
    while($arr[$size-1] <= $max) {
        dfs($arr);
        $arr[$size-1]++;
    }
}

function setHighScore($arr) {
    global $quad, $map, $highScore;
    $tmpScore = 0;
    for ($i=0; $i < $quad; $i++) { 
        $target = $map[$i];
        if ($arr[$target[1]]-$arr[$target[0]]==$target[2]) {
            $tmpScore+=$target[3];
        }
    }
    return max($tmpScore, $highScore);
}