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::str::FromStr;
use std::fmt::Debug;
use std::cmp;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()
}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn enum_pat(x: i64, n: usize, m: i64, cur: &mut Vec<i64>) -> Vec<Vec<i64>>{
    if cur.len() == n{
        return vec![cur.clone()];
    }

    let mut res = vec![];

    for i in x..=m{
        cur.push(i);
        let mut tmp = enum_pat(i, n, m, cur);
        res.append(&mut tmp);
        cur.pop();
    }

    return res;
}

fn main(){
    let line = read_as_vec::<usize>();
    let (n, m, q) = (line[0], line[1] as i64, line[2]);

    let mut x: Vec<(usize, usize, i64, usize)> = vec![];
    for _ in 0..q{
        let line = read_as_vec::<usize>();
        x.push((line[0]-1, line[1]-1, line[2] as i64, line[3]));
    }

    let mut tmp = vec![];
    let pats: Vec<Vec<i64>> = enum_pat(1, n, m, &mut tmp);

    let mut ans = 0;
    for pat in pats{
        let mut cur_ans = 0;
        for (a, b, c, d) in &x{
            if pat[*b] - pat[*a] == *c{
                cur_ans += d;
            }
        }
        ans = cmp::max(ans, cur_ans);
    }

    println!("{}",  ans);
}