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::Read;
use std::cmp::max;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let m: usize = iterator.next().unwrap().parse().unwrap();
    let q: usize = iterator.next().unwrap().parse().unwrap();
    let mut a: Vec<usize> = Vec::new();
    let mut b: Vec<usize> = Vec::new();
    let mut c: Vec<usize> = Vec::new();
    let mut d: Vec<usize> = Vec::new();
    for _ in 0..q {
        a.push(iterator.next().unwrap().parse().unwrap());
        b.push(iterator.next().unwrap().parse().unwrap());
        c.push(iterator.next().unwrap().parse().unwrap());
        d.push(iterator.next().unwrap().parse().unwrap());
    }

    let mut array: Vec<usize> = vec![0; n];
    let mut arrays: Vec<Vec<usize>> = Vec::new();
    dfs(0, n, m, &mut array, &mut arrays);

    let mut ans: usize = 0;
    for array in arrays.iter() {
        let mut score: usize = 0;
        for i in 0..q {
            if array[b[i] - 1] - array[a[i] - 1] == c[i] {
                score += d[i];
            }
        }
        ans = max(ans, score);
    }

    return ans.to_string()
}

fn dfs(i: usize, n: usize, m: usize, array: &mut Vec<usize>, arrays: &mut Vec<Vec<usize>>) {
    if i == n {
        arrays.push(array.clone());
        return;
    }

    let mut last: usize = if i == 0 {
        1
    } else {
        array[i - 1]
    };
    while last <= m {
        array[i] = last;
        dfs(i + 1, n, m, array, arrays);
        last += 1;
    }
}