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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

"use strict";

const main = arg => {
    const input = arg.trim().split("\n");

    const [N, M, Q] = input[0].split(" ").map(el => parseInt(el));
    let list = []
    for(let i = 1; i<=Q; i++){
        list.push(input[i].split(" ").map(el => parseInt(el)))
    }
    let ans = 0
    const dfs = function(parent, sub){
        if(sub.length == N){
            let tmp = 0
            for(let i = 0; i<Q; i++){
                if(sub[list[i][1]-1] - sub[list[i][0]-1] == list[i][2]){
                    tmp += list[i][3]
                }
            }
            ans = Math.max(ans, tmp)
            return
        }
        for(let i = parent; i<=M; i++){
            sub.push(i)
            dfs(i, sub)
            sub.pop()
        }
    }
    dfs(1, [])
    console.log(ans)
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));