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)

#[macro_use]extern crate text_io;
use proconio::input;

fn dfs<F>(v:&mut Vec::<i32>,n:i32,m:i32,dep:i32,max:&mut i32,checker:&F)
where F:Fn(&Vec::<i32>) -> i32
{
    if dep == n {
        *max = std::cmp::max(*max,checker(v));
        return;
    }
    for i in if dep == 0 {1}else{v[(dep-1) as usize]}..=m {
        v[dep as usize] = i;
        dfs(v,n,m,dep+1,max,checker);
    }
}

fn main() {
    input!(n:i32,m:i32,q:i32);
    let mut st = Vec::new();
    for _ in 0..q {
        input!(a:i32,b:i32,c:i32,d:i32);
        st.push((a,b,c,d));
    }
    let mut ar = Vec::new();
    for _ in 0..n {
        ar.push(1);
    }
    let check = |ag:&Vec<i32>|{
        let mut pt = 0;
        for (a,b,c,d) in st.iter() {
            if ag[(*b-1) as usize] - ag[(*a-1) as usize] == *c {pt += *d}
        }
        pt
    };
    let mut cnt = 0;
    dfs(&mut ar,n,m,0,&mut cnt,&check);
    println!("{}",cnt);
}