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 proconio::input;
use proconio::marker::Usize1;
use std::cmp::{max, min};
use im_rc::{vector, Vector};

type QT = (usize, usize, u64, u64);

fn main() {
    input! {
        n: usize,
        m: u64,
        q: usize,
        arr: [(Usize1, Usize1, u64, u64); q],
    }

    let mut solve = Solve {
        n,
        m,
        q,
        arr,
        ans: 0,
    };
    solve.solve();
}

struct Solve {
    n: usize,
    m: u64,
    q: usize,
    arr: Vec<QT>,
    ans: u64,
}

impl Solve {
    fn solve(&mut self) {
        self.dfs(vector![]);
        let ans = self.ans;
        println!("{}", ans);
    }

    fn dfs(&mut self, v: Vector<u64>) {
        if v.len() == self.n {
            let c = self.calc(&v);
            self.ans = max(self.ans, c);
            return;
        }

        let last = match v.last() {
            Some(x) => *x,
            None => 1,
        };

        for next in last..=self.m {
            let mut u = v.clone();
            u.push_back(next);
            self.dfs(u);
        }
    }

    fn calc(&self, v: &Vector<u64>) -> u64 {
        let mut ret = 0u64;
        for &(a, b, c, d) in &self.arr {
            if v[b] - v[a] == c {
                ret += d;
            }
        }

        ret
    }
}