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 Perl (5.26.1) (judge verdict: Accepted)

use List::Util qw(max min sum);

my ($n, $m, $q) = split(/\s+/, <>);
my (@a, @b, @c, @d);
for (1..$q) {
    ($a[$_],$b[$_],$c[$_],$d[$_]) = split(/\s+/, <>);
}

my @x;
for (0..$m) { $x[$_] = 1; }

sub ans {
    my $ret = 0;
    for (1..$q) {
	if ($x[$b[$_]]-$x[$a[$_]]==$c[$_]) {
	    $ret += $d[$_];
	}
    }
    return $ret;
}

my $max = 0;
sub loop {
    my ($level) = @_;
    if ($level == $n) {
	$max = max($max, ans());
	#print join(" ", @x), " max=$max\n";
	return;
    }
    for ($x[$level]..$m) {
	$x[$level+1] = $_;
	loop($level+1);
    }
    $x[$level+1] = $x[$level];
}

loop(0);
print "$max\n";