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;

fn main() {
    let vs: Vec<usize> = parse_values(3);
    let n: usize = vs[0];
    let m: usize = vs[1];
    let q: usize = vs[2];
    let mut q_vecs: Vec<Vec<usize>> = Vec::with_capacity(q);
    for _i in 0..q {
        let vecs: Vec<usize> = parse_values(4);
        q_vecs.push(vecs);
    }
    let mut max_score: usize = 0;
    for i in 1..=m {
        let score = solve(m, n, &mut vec![i], &q_vecs);
        max_score = max_score.max(score);
    }
    println!("{}", max_score);
}

fn solve(m: usize, n: usize, current: &Vec<usize>, q_vecs: &Vec<Vec<usize>>) -> usize {
    if current.len() == n {
        let a = current;
        let mut score: usize = 0;
        for q_vec in q_vecs {
            if a[q_vec[1]-1] - a[q_vec[0]-1] == q_vec[2] {
                score += q_vec[3];
            }
        }
        return score
    }
    let last = *current.last().unwrap();
    let mut max_score = 0;
    for i in 0..=m-last {
        let mut current_increased: Vec<usize> = current.iter().cloned().collect();
        current_increased.push(last+i);
        let score = solve(m, n, &current_increased, q_vecs);
        max_score = max_score.max(score);
    }
    max_score
}


#[allow(dead_code)]
fn parse_line<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn parse_values<T: std::str::FromStr>(n: usize) -> Vec<T> {
    let line = parse_line::<String>();
    let mut split = line.split_whitespace();
    let mut values = Vec::with_capacity(n);
    for _ in 0..n {
        let v = split.next().unwrap().parse::<T>().ok().unwrap();
        values.push(v);
    }
    values
}