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)

#!/usr/bin/perl

my ($n,$m,$q) = map { $_ - 0 } split(/\s+/,<STDIN>);

my @d = ();
for(my $i=0;$i<$q;$i++){
  my @du = map { $_ - 0 } split(/\s+/,<STDIN>);
  push(@d,\@du);
}

my $mx = 0;

my @st = ();
for(my $i=0;$i<$n;$i++){
  $st[$i] = 0;
}

while(1){
  #print ( join(":",@st) . "\n");
  my $sc = 0;
  for(my $k=0;$k<$q;$k++){
    if( $st[$d[$k]->[1]-1] - $st[$d[$k]->[0]-1] == $d[$k]->[2] ){
      $sc += $d[$k]->[3];
    }
  }
  
  if( $sc > $mx ){ $mx = $sc; }
  last unless &cup;
  
}
print "$mx\n";
exit(0);


for(my $i=1;$i<1024;$i++){
  my $sc = 0;
  my @aa = ();
  
  my $j = 1;
  for(my $k=0;$k<10;$k++){
    if( $j & $i ){
      push(@aa,$k);
    }
    $j += $j;
  }
  next unless $#aa == $n - 1;
  print (join(':',@aa) . "\n");
  
  for(my $k=0;$k<$q;$k++){
    if( $aa[$d[$k]->[1]-1] - $aa[$d[$k]->[0]-1] == $d[$k]->[2] ){
      $sc += $d[$k]->[3];
    }
  }
  
  if( $sc > $mx ){ $mx = $sc; }
}
print "$mx\n";

sub cup {
  my $i = $n - 1;
  my $c = 1;
  while( $i>=0 and $c > 0 ){
    $st[$i] += $c;
    $c = 0;
    if( $st[$i]>9 ){
      $c = 1;
      $st[$i] = $st[$i-1];
      $i--;
    }
  }
  return 0 if( $c>0 );
  #print ( "i=$i  " . join(',',@st) .  "\n");
  for(my $j=$i+1;$j<$n;$j++){
    $st[$j] = $st[$i];
  }
  #print ( "i=$i  " . join(',',@st) .  "\n");
  return 1;
}