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: Wrong Answer)

package main

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

var sc = bufio.NewScanner(os.Stdin)
var w = bufio.NewWriter(os.Stdout)

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

func main() {
    defer w.Flush()

    sc.Split(bufio.ScanWords)
    N := nextInt()
    M := nextInt()
    Q := nextInt()

    o := [][]int{}
    p := [][]int{}

    init := 0
    a := make([]int, N)
    for i := range a {
        a[i] = init + 1
    }

    t := make([]int, N)
    copy(t, a)
    o = append(o, t)
    for i := N - 1; i >= 0; i-- {
        for j := a[i]; j < M; j++ {
            a[i] = a[i] + 1

            t = make([]int, N)
            copy(t, a)
            o = append(o, t)
        }
    }

    u := make([]int, 4)
    for i := 0; i < Q; i++ {
        q := make([]int, 4)
        for j := range q {
            q[j] = nextInt()
        }
        u = make([]int, 4)
        copy(u, q)
        p = append(p, u)
    }

    max := 0
    total := 0

    for oi := range o {
        total = 0
        for pi := range p {
            if (o[oi][p[pi][1]-1] - o[oi][p[pi][0]-1]) == p[pi][2] {
                total = total + p[pi][3]
            }
        }
        if total > max {
            max = total
        }
    }
    fmt.Fprintln(w, max)
}