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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

      module piyoMod
      implicit none
      integer(16) :: n,m,q,ans=0
      integer(16),allocatable :: abcd(:,:)
      
      contains
      recursive subroutine solve( cnt,array )
        implicit none
        integer(16),intent(in) :: cnt,array(:)
        integer(16) :: a(size(array)), i,buffer
        
        a = array
        if( cnt==1 )then
          do i = 1,m
            a(1) = i
            call solve( cnt+1,a )
          end do
        else if( cnt==n+1 )then
          
          !calc ans
          buffer = 0
          do i = 1,q
            if( a(abcd(i,2))-a(abcd(i,1))==abcd(i,3) )then
              buffer = buffer + abcd(i,4)
            end if
          end do
          ans = max( ans,buffer )
          
        else
          do i = a(cnt-1),m
            a(cnt) = i
            call solve( cnt+1,a )
          end do
        end if
      end subroutine
        
      
      end module
      
      PROGRAM ManyRequirments
      use piyoMod
      IMPLICIT NONE
      integer(16) :: i,dummy(10)
      
      read*,n,m,q
      allocate( abcd(q,4) )
      do i = 1,q
        read*,abcd(i,:)
      end do
      
      call solve(1_16,dummy(1:n))
      print*,ans
      
      
      
      
      END PROGRAM