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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

//Util
func nextStr() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

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

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

func absInt(a int) int {
	if a >= 0 {
		return a
	} else {
		return -a
	}
}

//Main
var sc = bufio.NewScanner(os.Stdin)

var n, m, q int

var pairs [][]int

//https://youtu.be/C5_NnCp1CRI?t=1778
//組み合わせを全部列挙
func dfs(A []int) int {
	if len(A) == n+1 {
		var sum int
		for _, p := range pairs {
			if A[p[1]]-A[p[0]] == p[2] {
				sum += p[3]
			}
		}
		return sum
	}

	var ans int
	for i := 1; i <= m; i++ {
		//1つ前が、iより大きい場合はスキップ
		if A[len(A)-1] > i {
			continue
		}
		ans = maxInt(dfs(append(A, i)), ans)
	}
	return ans
}

func main() {
	sc.Split(bufio.ScanWords)
	n, m, q = nextInt(), nextInt(), nextInt()
	for i := 0; i < q; i++ {
		pair := make([]int, 4)
		pair[0], pair[1], pair[2], pair[3] = nextInt(), nextInt(), nextInt(), nextInt()
		pairs = append(pairs, pair)
	}

	//dfsの処理がしやすいように、[1]で初期化
	A := []int{1}
	fmt.Println(dfs(A))
	//fmt.Println(N, M, Q, pairs)

}