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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
)

var n, m, q int
var abcd [][]int
var arrs [][]int

func main() {
	fmt.Scan(&n, &m, &q)
	create(1, []int{})
	ans := 0
	abcd = make([][]int, q)
	for i := 0; i < q; i++ {
		abcd[i] = make([]int, 4)
		fmt.Scan(&abcd[i][0], &abcd[i][1], &abcd[i][2], &abcd[i][3])
	}
	for _, arr := range arrs {
		score := 0
		for _, seq := range abcd {
			if arr[seq[1]-1]-arr[seq[0]-1] == seq[2] {
				score += seq[3]
			}
		}
		if score > ans {
			ans = score
		}
	}
	fmt.Println(ans)
}

func create(i int, arr []int) {
	if len(arr) == n {
		arrs = append(arrs, arr)
		return
	}
	if i > m {
		return
	}
	create(i+1, append([]int{}, arr...))
	create(i+1, append(arr, i))
}