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;

struct SeqIterator {
  stack : Vec<(usize, usize)>,
  n : usize,
  m : usize,
  seq : [usize; 11],
}

impl SeqIterator {
  fn new(n: usize, m : usize) -> SeqIterator {
    SeqIterator{ n, m, seq: [0; 11], stack : vec![(0,1)] }
  } 
}

impl Iterator for SeqIterator {
  type Item = Vec<usize>;
  fn next(&mut self) -> Option<Self::Item> {
    let n = self.n;
    let m = self.m;
    let stack = &mut self.stack;
    let seq = &mut self.seq;
    
    loop {
      let (i,j) = stack.pop()?;
      seq[i] = j;
      
      if i == n {
        break Some(seq[0 ..= n].to_vec());
      }
      
      for k in j ..= m {
        stack.push((i + 1, k));
      }
    }
  }
}

fn main() {
  input!{
      n: usize,
      m: usize,
      q: usize,
      qu: [(usize, usize, usize, i32); q]
  };
  let ans : i32 = SeqIterator::new(n, m)
  	.map(|seq| qu.iter().map(|&(a,b,c,d)| if seq[b] - seq[a] == c { d } else { 0 } ).sum())
  	.max()
  	.unwrap();
  println!("{}", ans);
}