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 proconio::input;
use proconio::marker::Usize1;

struct ToCulc<'a> {
  N: usize,
  M: usize,
  Q: usize,
  A: &'a [(usize, usize, usize, usize)],
  max: usize
}

impl <'a>ToCulc<'a> {
  pub fn culc(&mut self, inner_stack: &mut Vec<usize>) {
    if inner_stack.len() == self.N + 1 {
      let mut temp = 0;
      for j in self.A.iter() {
        if inner_stack[j.1] - inner_stack[j.0] == j.2 {
          temp += j.3;
        }
      }
      self.max = std::cmp::max(self.max, temp);
      return
    }
    
    let last_len = inner_stack.len() - 1;
    while inner_stack[last_len] <= self.M {
      let mut new_stack = inner_stack.clone();
      new_stack.push(*new_stack.last().unwrap());
      self.culc(&mut new_stack);
      inner_stack[last_len] += 1;
    }
  }
}

fn main() {
  input! {
    N: usize,
    M: usize,
    Q: usize,
    A: [(Usize1, Usize1, usize, usize);Q]
  }
  
  let mut to_culc = ToCulc {
    N, M, Q, A: &A, max: 0
  };
  
  let mut stack: Vec<usize> = vec![1];
  to_culc.culc(&mut stack);
  
  println!("{}", to_culc.max);
}