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: Wrong Answer)

program sum
    implicit none
    integer i,j,n,m,q,a(10),d(50,4),c,score,score1,flag
    read(*,*) n,m,q
    c=1
    score=0
    score1=0
    flag=0
    do i = 1, q
        read(*,*) d(i,1),d(i,2),d(i,3),d(i,4)
    end do
    do i = 1, n
        c=c*(11-i)
    end do
    do i = 2, n
        c=c/i
    end do
    do i = 1, n
        a(i)=i
    end do
    do while (a(n)<=10)
        ! do i = 1, n
        !     write(*, fmt='(I4)', advance='no') a(i)
        ! end do
        ! Write(*,*)
        do j = 1, q
            if ( a(d(j,2))-a(d(j,1))==d(j,3) ) then
                score=score+d(j,4)
            end if
        end do
        if ( score>score1 ) then
            score1=score
        end if
        score=0
        a(n-flag)=a(n-flag)+1
        if ( flag==n-1 ) then
            flag=0
        else
            flag=flag+1
        end if
    end do
    write(*,*) score1
end program sum