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 Rust (1.42.0) (judge verdict: Accepted)

use std::io;
use std::str::FromStr;
use std::collections::HashSet;

type Question = (u64, u64, u64, u64);

fn input_tuple() -> (u64, u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1], vec[2])
}

fn input_tuple_4() -> (u64, u64, u64, u64) {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    let vec: Vec<u64> = line.split_whitespace().map(|s| s.parse().unwrap()).collect();
    (vec[0], vec[1], vec[2], vec[3])
}

fn dfs(idx: usize, a_vec: &Vec<u64>, n: u64, m: u64, questions: &Vec<Question>) -> u64 {
    if idx == n as usize {
        let mut sum = 0;
        for q in questions {
            if a_vec[q.1 as usize] - a_vec[q.0 as usize] == q.2 {
                sum += q.3
            }
        }
        return sum;
    }
    let num: u64;
    if idx == 0 {
        num = 1;
    } else {
        num = a_vec[idx - 1];
    }
    let mut ans: u64;
    let mut max = 0;
    for i in num..(m+1) {
        let mut new_vec = a_vec.to_vec();
        new_vec.push(i);
        ans = dfs(idx+1, &new_vec, n, m, questions);
        if ans > max {
            max = ans;
        }
    }
    return max;
}



fn main() {
    let (n, m, q) = input_tuple();
    let mut questions: Vec<Question> = Vec::new();
    for _ in 0..q {
        let (a, b, c, d) = input_tuple_4();
        questions.push((a-1, b-1, c, d));
    }
    println!("{}", dfs(0, &Vec::new(), n, m, &questions));

}