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::stdin;
use std::str::FromStr;
use std::cmp::max;

fn read_line<T>() -> Vec<T>
where
    T: FromStr,
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect()
}

fn read_str_as_char_vec() -> Vec<char> {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    s.trim().chars().collect()
}

fn read_str_as_T<T>() -> T 
where
    T: FromStr,
    <T as std::str::FromStr>::Err: std::fmt::Debug,
{
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    s.trim().parse().unwrap()
}

fn main() {
    let in_vec: Vec<usize> = read_line();
    let n = in_vec[0];
    let m = in_vec[1];
    let q = in_vec[2];

    // $B0lC6(B 10 $B=E%k!<%W$G5a$a$F$_$k(B
    let mut reps = Vec::<(usize, usize, usize, usize)>::new();
    for _i in 0..q {
        let in_vec: Vec<usize> = read_line();
        reps.push((in_vec[0], in_vec[1], in_vec[2], in_vec[3]));
    }

    let mut res = 0;
    for l0 in 1..m+1 {
        for l1 in l0..=m {
            for l2 in l1..=m {
                for l3 in l2..=m {
                    for l4 in l3..=m {
                        for l5 in l4..=m {
                            for l6 in l5..=m {
                                for l7 in l6..=m {
                                    for l8 in l7..=m {
                                        for l9 in l8..=m {
                                            let mut temp = 0;
                                            let state = vec![l0, l1, l2, l3, l4, l5, l6, l7, l8, l9];
                                            for &(a, b, c, d) in reps.iter() {
                                                if state[b-1] - state[a-1] == c {
                                                    temp += d;
                                                }
                                            }
                                            res = max(res, temp);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }

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