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)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn calc(abcdv: &Vec<Vec<u32>>, v: &mut Vec<u32>, ans: &mut u32) {
    let mut tmp = 0;

    for i in 0..abcdv.len() {
        let a = abcdv[i][0] as usize;
        let b = abcdv[i][1] as usize;
        let c = abcdv[i][2];
        let d = abcdv[i][3];

        if v[b] - v[a] == c {
            tmp += d;
        }
    }

    if tmp > *ans {
        *ans = tmp;
    }
}

fn rec(n: usize, m: u32, abcdv: &Vec<Vec<u32>>, v: &mut Vec<u32>, ans: &mut u32) {
    if n == 0 {
        calc(abcdv, v, ans);
    } else {
        let l = v[v.len() - 1];
        for tmp in l..m + 1 {
            v.push(tmp);
            rec(n - 1, m, abcdv, v, ans);
            v.pop();
        }
    }
}

fn main() {
    let nmq: Vec<u32> = read_vec();
    let n = nmq[0] as usize;
    let m = nmq[1];
    let q = nmq[2] as usize;

    let abcdv: Vec<Vec<u32>> = read_vec2(q);

    let mut v = vec![1];

    let mut ans = 0;

    rec(n, m, &abcdv, &mut v, &mut ans);

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