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)

package main

import "fmt"

var n, m, q, ans int
var a, b, c, d []int

func calc(nums []int) int {
	ret := 0
	for i := 0; i < q; i++ {
		if nums[b[i]]-nums[a[i]] == c[i] {
			ret += d[i]
		}
	}
	return ret
}

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

func dfs(a []int, step int) {
	if step == n {
		// fmt.Println("a", a, "score", calc(a))
		ans = max(ans, calc(a))
		return
	}
	var s int
	if step == 0 {
		s = 1
	} else {
		s = a[len(a)-1]
	}
	for i := s; i <= m; i++ {
		dfs(append(a, i), step+1)
	}
}

func main() {
	fmt.Scan(&n, &m, &q)
	a = make([]int, q)
	b = make([]int, q)
	c = make([]int, q)
	d = make([]int, q)
	for i := 0; i < q; i++ {
		fmt.Scan(&a[i], &b[i], &c[i], &d[i])
		a[i]--
		b[i]--
	}
	dfs([]int{}, 0)
	fmt.Println(ans)
}