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)

fn dfs(
    n: usize,
    lb: usize,
    ub: usize,
    target: &mut Vec<usize>,
    abcds: &Vec<(usize, usize, usize, usize)>,
) -> usize {
    // 集計
    if n == 0 {
        let mut res = 0;
        for e in abcds {
            if target[e.1] - target[e.0] == e.2 {
                res += e.3;
            }
        }
        return res;
    } else {
        let mut res = 0;
        for z in lb..ub + 1 {
            target.push(z);
            res = max(dfs(n - 1, z, ub, target, abcds), res);
            target.pop();
        }
        return res;
    }
}

fn solve() {
    let (n, m, q): (usize, usize, usize) = (read::<usize>(), read::<usize>(), read::<usize>());
    let mut abcds = vec![];
    for _ in 0..q {
        let (a, b, c): (usize, usize, usize) =
            (read::<usize>() - 1, read::<usize>() - 1, read::<usize>());
        let d: usize = read();
        abcds.push((a, b, c, d));
    }
    let mut target = Vec::with_capacity(n);
    println!("{}", dfs(n, 1, m, &mut target, &abcds));
}

fn main() {
    let stack_size = 104_857_600;
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min, Reverse};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1000000007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// =========