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)

#![allow(unused)]

//==============================================================================
//
// Boilerplate code
//
//==============================================================================

macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

//
// Based on EbTech's Scanner https://stackoverflow.com/q/56449027
//
struct Scanner<'a, R: std::io::BufRead> {
    reader: R,
    buf: String,
    iter: std::str::SplitWhitespace<'a>,
}

impl<'a, R: std::io::BufRead> Scanner<'a, R> {
    fn new(reader: R) -> Self {
        Self { reader, buf: String::new(), iter: "".split_whitespace() }
    }

    fn get<T: std::str::FromStr>(&mut self) -> T {
        if let Some(t) = self.iter.next() {
            return t.parse().ok().expect("Parse error")
        }
        self.buf.clear();
        self.reader.read_line(&mut self.buf).expect("I/O error");
        self.iter = unsafe { std::mem::transmute(self.buf.split_whitespace()) };
        self.get()
    }

    fn gets<T: std::iter::FromIterator<char>>(&mut self) -> T {
        use std::io::Read;
        assert_eq!(self.iter.next(), None);
        self.reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap() as char)
            .skip_while(|&c| c.is_whitespace())
            .take_while(|&c| !c.is_whitespace())
            .collect()
    }
}

fn main() {
    let stdin = std::io::stdin();
    solve(Scanner::new(stdin.lock()));
}

//==============================================================================
//
// Problem-specific code
//
//==============================================================================

fn combinations_with_replacement<F: FnMut(&Vec<i64>)>(
    (min, max): (i64, i64),
    n: usize,
    mut f: F
) {
    fn go<F: FnMut(&Vec<i64>)>(
        pos: usize,
        seq: &mut Vec<i64>,
        (min, max): (i64, i64),
        n: usize,
        f: &mut F
    ) {
        if pos == n {
            f(seq);
            return;
        }
        let start = if pos == 0 { min } else { seq[pos - 1] };
        for i in start..=max {
            seq[pos] = i;
            go(pos + 1, seq, (min, max), n, f);
        }
    }

    let mut seq = vec![0; n];
    go(0, &mut seq, (min, max), n, &mut f);
}

fn eval(seq: &Vec<i64>, constrs: &Vec<(usize, usize, i64, i64)>) -> i64 {
    constrs.iter()
        .map(|&(a, b, c, d)| if seq[b - 1] - seq[a - 1] == c { d } else { 0 })
        .sum()
}

fn solve<R: std::io::BufRead>(mut sc: Scanner<R>) {
    let n = sc.get();
    let m = sc.get();
    let q = sc.get();
    let constrs: Vec<(usize, usize, i64, i64)> =
        (0..q).map(|_| (sc.get(), sc.get(), sc.get(), sc.get())).collect();

    let mut ans = 0;
    combinations_with_replacement((1, m), n, |seq| {
        ans = std::cmp::max(ans, eval(seq, &constrs));
    });

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