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: Runtime Error)

package main

import (
	"fmt"
)

type Set [4]int

func main() {
	var m, n, q int
	fmt.Scanf("%d %d %d", &m, &n, &q)

	setList := make([]Set, q)
	for i := 0; i < q; i++ {
		fmt.Scanf("%d %d %d %d", &setList[i][0], &setList[i][1], &setList[i][2], &setList[i][3])
	}

	score := solve(make([]int, n), m, setList, 0)

	fmt.Printf("%d\n", score)
}

func solve(a []int, m int, setList []Set, deps int) int {
	if deps >= len(a) - 1 {
		return calcScore(a, setList)
	}
	nextDeps := deps+1
	max := 0
	for i := a[deps]; i <= m; i++ {
		nextA := a
		nextA[nextDeps] = i
		score := solve(nextA, m, setList, nextDeps)
		if max < score {
			max = score
		}
	}
	return max
}

func calcScore(a []int, setList []Set) int {
	var score int
	for _, set := range setList {
		if a[set[1] - 1] - a[set[0] - 1] == set[2] {
			score += set[3]
		}
	}
	return score
}