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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

long int check(int Q, int A[], long int Group[][4])
{
  long int ans=0;
  for (int i = 0; i< Q; i++) {
    if (A[Group[i][1]] - A[Group[i][0]] == Group[i][2])
      ans += Group[i][3];
  }
  return ans;
}

int main(void)
{
  int N, M, Q;
  int ii, j, k, l, m, n, o, p, q, r;
  scanf("%d%d%d", &N, &M, &Q);
  int A[1+10];
  long int Group[Q][4], ans=0, tmp_ans=0;

  for (int i = 0; i < Q; i++) {
    for (int j = 0; j < 4; j++)
      scanf("%ld", &Group[i][j]);
  }

  /*A[N] combination*/
  
  for (ii = 0;ii < M; ii++) {
    A[1] = ii+1;
    for (j = ii; j < M; j++) {
    A[2] = j+1;
    for (k = j; k < M; k++) {
    A[3] = k+1;
    for (l = k; l < M; l++) {
    A[4] = l+1;
    for (m = l; m < M; m++) {
    A[5] = m+1;
    for (n = l; n < M; n++) {
    A[6] = n+1;
    for (o = n; o < M; o++) {
    A[7] = o+1;
    for (p = o; p < M; p++) {
    A[8] = p+1;
    for (q = p; q < M; q++) {
    A[9] = q+1;
    for (r = q; r < M; r++) {
    A[10] = r+1;
    if ((tmp_ans = check(Q, A, Group)) > ans)
      ans = tmp_ans;
    }}}}}}}}}}
  




    printf("%ld\n", ans);

    return 0;
}