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: Runtime Error)

{-# LANGUAGE PartialTypeSignatures #-}
module Main (main) where

import Data.Array
import Control.Monad
import qualified Data.ByteString.Char8 as C8
import qualified Data.Char as C
import qualified Data.List as L

main :: IO ()
main = do
  [n,m,q] <- readInts
  replicateM q readInts >>= output . solve n m

solve :: Int -> Int -> [[Int]] -> _
solve n m xs = maximum . map go $ genAscList m n
  where
    go as =
      let arr = listArray (1,n) as
       in sum [ d | [a,b,c,d] <- xs, (arr!(b-1)) - (arr!(a-1)) == c ]

genAscList :: Int -> Int -> [[Int]]
genAscList = gen 1
  where
    gen _ m 0 = [ [] ]
    gen a m n = [ i:is | i <- [a..m], is <- gen i m (pred n) ]

output :: _ -> IO ()
output = print

-- utils
readInts :: IO [Int]
readInts = L.unfoldr (C8.readInt . C8.dropWhile C.isSpace) <$> C8.getLine