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")
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let q: usize = read();
    let q_taple: Vec<(i32, i32, i32, i32)> =
        (0..q).map(|_| (read(), read(), read(), read())).collect();
    //let mut a: Vec<Vec<i32>> = vec![Vec::new(); n];
    let mut ans = 0;

    /*
    for i in q_taple.iter() {
        for j in 1..=m {
            for k in 1..=m {
                if i.2 == (j as i32 - k as i32) {
                    a[i.0 as usize - 1].push(k as i32);
                    a[i.1 as usize - 1].push(j as i32);
                }
            }
        }
    }
    */

    for i1 in 1..m + 1 {
        for i2 in i1..m + 1 {
            for i3 in i2..m + 1 {
                for i4 in i3..m + 1 {
                    for i5 in i4..m + 1 {
                        for i6 in i5..m + 1 {
                            for i7 in i6..m + 1 {
                                for i_8 in i7..m + 1 {
                                    for i9 in i_8..m + 1 {
                                        for i10 in i9..m + 1 {
                                            let mut tmp = 0;
                                            let arrs =
                                                [0, i1, i2, i3, i4, i5, i6, i7, i_8, i9, i10];
                                            for j in q_taple.iter() {
                                                if j.2
                                                    == arrs[j.1 as usize] as i32
                                                        - arrs[j.0 as usize] as i32
                                                {
                                                    tmp += j.3;
                                                }
                                                ans = std::cmp::max(ans, tmp);
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
    }

    //println!("{:?}", q_taple);
    //println!("{:?}", a);
    println!("{}", ans);
}