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)

macro_rules! l {
    () => {{
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim()
            .split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect::<Vec<i32>>()
    }};
}

struct A<'a> {
    m: i32,
    v: Vec<i32>,
    check: Box<dyn FnMut(&Vec<i32>) + 'a>,
}

impl A<'_> {
    fn dfs(&mut self, i: usize, cm: i32) {
        if self.v.len() == i {
            (self.check)(&self.v);
            return;
        }
        for x in cm..(self.m + 1) {
            self.v[i] = x;
            self.dfs(i + 1, x);
        }
    }
}

fn main() {
    let (n, m, q) = match &l!()[..] {
        &[n, m, q] => (n, m, q),
        _ => panic!(),
    };

    let reqs = (0..q).into_iter().map(|_| l!()).collect::<Vec<_>>();

    let mut ans = -1;
    {
        let mut a = A {
            m: m,
            v: vec![-1; (1 + n) as usize],
            check: Box::new(|v| {
                let mut sum = 0;
                for r in &reqs {
                    if v[r[1] as usize] - v[r[0] as usize] == r[2] {
                        sum += r[3];
                    }
                }
                ans = std::cmp::max(sum, ans);
            }),
        };
        a.dfs(1, 1);
    }

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