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: Accepted)

// なんだこれ Aを決め打ちするのか？まにあうんかそれ
package main

import "fmt"

var N, M, Q int
var AS [][]int

func main() {
	fmt.Scan(&N, &M, &Q)
	AS = [][]int{}
	for i := 1; i <= M; i++ {
		a := []int{i}
		createAS(a)
	}
	queries := make([][]int, Q)
	for i := 0; i < Q; i++ {
		var a, b, c, d int
		fmt.Scan(&a, &b, &c, &d)
		queries[i] = []int{a, b, c, d}
	}
	ans := 0
	for _, a := range AS {
		tmp_ans := 0
		for _, q := range queries {
			if a[q[1]-1]-a[q[0]-1] == q[2] {
				tmp_ans += q[3]
			}
		}
		ans = max(ans, tmp_ans)
	}
	fmt.Println(ans)
}

func max(a, b int) int {
	if a < b {
		return b
	}
	return a
}

func createAS(arr []int) {
	if len(arr) == N {
		tes := append([]int{}, arr...)
		AS = append(AS, tes)
	} else {
		limit := arr[len(arr)-1]
		tmp_arr := append([]int{}, arr...)
		for i := limit; i <= M; i++ {
			tmp_arr = append(tmp_arr, i)
			createAS(tmp_arr)
			tmp_arr = tmp_arr[:len(tmp_arr)-1]
		}
	}

}