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;


struct State {
    n: usize,
    m: i64,
    q: usize,
    a: Vec<usize>,
    b: Vec<usize>,
    c: Vec<i64>,
    d: Vec<i64>,
}

impl State {
    fn dfs(&self, cur: &mut Vec<i64>, i: usize) -> i64 {
        if i == self.n {
            let mut ans = 0;
            for j in 0..self.q {
                if cur[self.b[j]] - cur[self.a[j]] == self.c[j] {
                    ans += self.d[j];
                }
            }
            return ans;
        }
        let minimum = if i == 0 { 1 } else { cur[i - 1] };
        let maximum = self.m;
        let mut ans = 0;
        for v in minimum..=maximum {
            cur[i] = v;
            ans = std::cmp::max(ans, self.dfs(cur, i + 1));
        }
        ans
    }

    fn solve(&self) -> i64{
        let mut cur = vec![0; self.n];
        self.dfs(&mut cur, 0)
    }
}

fn main() {
    let mut line = String::new();
    std::io::stdin().read_to_string(&mut line);
    let mut iter = line.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let m: i64 = iter.next().unwrap().parse().unwrap();
    let q: usize = iter.next().unwrap().parse().unwrap();
    let mut a: Vec<usize> = vec![];
    let mut b: Vec<usize> = vec![];
    let mut c: Vec<i64> = vec![];
    let mut d: Vec<i64> = vec![];
    for _ in 0..q {
        a.push(iter.next().unwrap().parse::<usize>().unwrap() - 1);
        b.push(iter.next().unwrap().parse::<usize>().unwrap() - 1);
        c.push(iter.next().unwrap().parse().unwrap());
        d.push(iter.next().unwrap().parse().unwrap());
    }
    let mut solver = State {
        n,
        m,
        q,
        a,
        b,
        c,
        d,
    };
    println!("{}", solver.solve());
}