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: Runtime Error)

use itertools::Itertools;

fn main() {
    let (n, m, q, v) = input();
    println!("{}", solve(n, m, q, v));
}

fn input() -> (usize, usize, usize, Vec<(usize, usize, usize, usize)>) {
    let mut buf1 = String::new();
    let mut buf2 = String::new();
    
    std::io::stdin().read_line(&mut buf1).unwrap();
    std::io::stdin().read_line(&mut buf2).unwrap();
    buf1.pop();
    buf2.pop();
    let mut iter1 = buf1.split_whitespace();
    let mut iter2 = buf2.split_whitespace();

    let n: usize = iter1.next().unwrap().parse().unwrap();
    let m: usize = iter1.next().unwrap().parse().unwrap();
    let q: usize = iter2.next().unwrap().parse().unwrap();

    let mut v: Vec<(usize, usize, usize, usize)> = Vec::new();
    for _ in 0..q {
        let mut buf3 = String::new();
        std::io::stdin().read_line(&mut buf3).unwrap();
        buf3.pop();
        let mut iter3 = buf3.split_whitespace();
        let a: usize = iter3.next().unwrap().parse().unwrap();
        let b: usize = iter3.next().unwrap().parse().unwrap();
        let c: usize = iter3.next().unwrap().parse().unwrap();
        let d: usize = iter3.next().unwrap().parse().unwrap();
        v.push((a, b, c, d));
    }
    (n, m, q, v)
}

fn solve(n: usize, m: usize, q: usize, v: Vec<(usize, usize, usize, usize)>) -> usize {
    let t = (1..m).combinations_with_replacement(n)
            .map(|A| 
                v.iter()
                .filter(|(a, b, c, _d)| A[*b-1] - A[*a-1] == *c )
                .fold(0, |sum, (_, _, _, d)| sum + d )
            );
    t.max().unwrap()
}