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::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = 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")
}
#[allow(dead_code)]
struct Main {
    n: usize,
    m: usize,
    q: usize,
    ptns: Vec<Vec<usize>>,
    a: Vec<usize>,
    b: Vec<usize>,
    c: Vec<usize>,
    d: Vec<usize>,
    max: usize,
}

#[allow(dead_code)]
impl Main {
    fn dfs(&mut self, vals: Vec<usize>, depth: usize) {
        if depth == self.n {
            return;
        }
        if depth == self.n - 1 {
            // println!("{:?}", vals);
            let mut sum = 0;
            for i in 0..self.q {
                let expected_c = vals[self.b[i]] - vals[self.a[i]];
                if expected_c == self.c[i] {
                    // println!("{}", self.d[i]);
                    sum += self.d[i];
                }
            }
            // println!("{:?}", sum);
            if sum > self.max {
                self.max = sum;
            }
        }

        for new_val in *vals.last().unwrap()..=self.m {
            let mut next_vals = vals.clone();
            next_vals.push(new_val);
            self.dfs(next_vals, depth + 1);
        }
    }
    fn invoke(&mut self) {
        self.dfs(vec![1], 0);
        println!("{}", self.max);
    }
}

fn main() {
    let n = read::<usize>();
    let m = read::<usize>();
    let q = read::<usize>();
    let mut a = vec![0; q];
    let mut b = vec![0; q];
    let mut c = vec![0; q];
    let mut d = vec![0; q];
    for i in 0..q {
        let a_one = read::<usize>();
        a[i] = a_one - 1;
        let b_one = read::<usize>();
        b[i] = b_one - 1;
        let c_one = read::<usize>();
        c[i] = c_one;
        let d_one = read::<usize>();
        d[i] = d_one;
    }
    Main {
        n,
        m,
        q,
        ptns: vec![],
        a,
        b,
        c,
        d,
        max: 0,
    }
    .invoke();
}