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::{fastout, input};

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

struct Input {
    N: usize,
    M: usize,
    qs: Vec<(usize, usize, usize, usize)>,
}

fn go(v: &mut Vec<usize>, input: &Input) -> usize {
    if v.len() == input.N + 1 {
        let mut res = 0;
        for q in &input.qs {
            let (a, b, c, d) = q;
            if v[*b] - v[*a] == *c {
                res += *d;
            }
        }
        res
    } else {
        let mut res = 0;
        for i in (*v.last().unwrap())..=input.M {
            let mut p = v.clone();
            p.push(i);
            res = max(res, go(&mut p, &input));
        }
        res
    }
}

#[fastout]
fn main() {
    input! {
        N: usize,
        M: usize,
        Q: usize,
        qs: [(usize, usize, usize, usize); Q],
    }

    let input = Input { N, M, qs };

    let mut u = vec![1];
    let ans = go(&mut u, &input);
    println!("{}", ans);
}