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::cmp;
use std::collections::*;

pub struct Scanner {
    line: Vec<String>,
    idx: usize,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        return Scanner {
            line: vec![],
            idx: 0,
        };
    }
    fn next<T: std::str::FromStr>(&mut self) -> T {
        if self.idx == self.line.len() {
            let mut buffer = String::new();
            std::io::stdin().read_line(&mut buffer).ok();
            let a: Vec<&str> = buffer.trim().split(' ').collect();
            self.line = a.iter().map(|&s| String::from(s)).collect();
            self.idx = 0;
        }
        let ret: T = self.line[self.idx].parse::<T>().ok().expect("Parse error.");
        self.idx += 1;
        ret
    }
    fn next_string(&mut self) -> Vec<char> {
        let s: String = self.next();
        return s.chars().collect::<Vec<char>>();
    }
    fn next_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut v: Vec<T> = Vec::with_capacity(n);
        for _i in 0..n {
            v.push(self.next());
        }
        v
    }
}



fn main(){
    let mut scan = Scanner::new();
    let n: usize = scan.next();
    let m: usize = scan.next();
    let q: usize = scan.next();
    let mut sc: Vec<(usize,usize,usize,i32)> = Vec::with_capacity(q);
    for _ in 0..q {
        let a: usize = scan.next();
        let b: usize = scan.next();
        let c: usize = scan.next();
        let d: i32 = scan.next();
        sc.push((a,b,c,d));
    }

    let mut deq: VecDeque<Vec<usize>> = VecDeque::new();
    let mut ans = 0;
    deq.push_back(vec![1]);

    while let Some(v) = deq.pop_front(){
        if v.len() == n {
            let mut score = 0;
            for i in 0..q{
                if v[sc[i].1-1] - v[sc[i].0 - 1] == sc[i].2 {
                    score += sc[i].3;
                }
            }
            ans = cmp::max(ans, score);
        }else{
            let last = v[v.len()-1];
            for d in last..m+1 {
                let mut vv = v.clone();
                vv.push(d);
                deq.push_back(vv);
            }
        }
    }
    
    println!("{}", ans);
}