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: Wrong Answer)

use strict;
my $s = <STDIN>;
chomp $s;
my ($N,$M,$Q) = split(/ /,$s);
my @data;
for(my $i=0;$i<$Q;$i++){
    $s = <STDIN>;
    chomp $s;
    my @dat = split(/ /,$s);
    $data[$i] = \@dat;
}
my @list;
for(my $j=0;$j<$M;$j++){
  $list[$j][0] = 0;
}
for(my $j=0;$j<$M;$j++){
  $list[$j][0] = $j+1;
}
for(my $i=1; $i<$N;$i++){
 my @newlist;
 for(my $j=0;$j<=$#list;$j++){
   for(my $k=0; $k<=$N;$k++){
     my @new = @{$list[$j]};
     if(($new[-1]+$k) >$M){last;}
     push (@new, $new[-1]+$k);
     push (@newlist,\@new);
   }
  }
  @list = @newlist;
}
my $max=0;
for(my $j=0;$j<=$#list;$j++){
  #print "TG  @{$list[$j]}\n";
  my $point = 0;
  for(my $i=0;$i<$Q;$i++){
    my $a =    $data[$i][0];
    my $b =    $data[$i][1];  
    #print "($list[$j][$b-1]-$list[$j][$a-1])==$data[$i][2]  \n";  
    if( ($list[$j][$b-1]-$list[$j][$a-1])==$data[$i][2]){
        $point = $point + $data[$i][3];
        #print " get $point  "
    }
  }
   #print "pont $point\n";
  if($point > $max ){
      #print "max $point\n";
      $max = $point;
  }
}
print "$max\n";