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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

import Control.Monad
import Data.List as L

data ABCD = Input { a :: Int,
b :: Int,
c :: Int,
d :: Int } deriving (Show)

toAbcd :: [Int] -> ABCD
toAbcd input = case input of
  a:b:c:d:_ -> Input a b c d

patterns :: Int -> Int -> Int -> [[Int]]
patterns 0 _ _ = [[]]
patterns rest start end = concat $ map (\a -> map (\b -> a : b) $ patterns (rest-1) a end) [start..end]

score :: [ABCD] -> [Int] -> Int
score inputs pattern = foldl (\acc cur -> if (pattern !! ((b cur) - 1)) - (pattern !! ((a cur) - 1)) == (c cur)
  then acc + d cur
  else acc) 0 inputs

main=do
  (n:m:q:_)<-L.map read . words<$>getLine::IO[Int]
  inputs <- map toAbcd <$> forM [1..q] (\_-> L.map read . words<$> getLine::IO[Int])
  print $ maximum $ map (\a -> score inputs a) $ patterns n 1 m