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

var si = bufio.NewScanner(os.Stdin)

func readInt() int {
	si.Scan()
	r, _ := strconv.Atoi(si.Text())
	return r
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func calc(Q int, q [50][4]int, n, m int, a []int) int {
	ret := 0
	if n == 0 {
		for i := 0; i < Q; i++ {
			if a[q[i][1]]-a[q[i][0]] == q[i][2] {
				ret += q[i][3]
			}
		}
		return ret
	}
	for i := a[len(a)-1]; i <= m; i++ {
		ret = max(ret, calc(Q, q, n-1, m, append(a, i)))
	}
	return ret
}

func main() {
	si.Split(bufio.ScanWords)
	si.Buffer(make([]byte, 0), 10000000)
	N, M, Q := readInt(), readInt(), readInt()

	var q [50][4]int

	for i := 0; i < Q; i++ {
		q[i] = [4]int{readInt(), readInt(), readInt(), readInt()}
	}
	fmt.Println(calc(Q, q, N-1, M, []int{1}))

}