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)

getInts = do
  x <- getLine
  let y = (map$toInt)$words x
  return y
    where
      toInt x = read x ::Int
getMat x
  |x==1 = do
    y <- getInts
    return [y]
  |otherwise = do
    y <- getInts
    z <- getMat (x-1)
    let w = [y] ++ z
    return w

-- [Char]あるいは String を Int にする
toInt :: (String -> Int)
toInt x = read x ::Int

score::[Int]->[Int]->Int
score x abcd
  |(x!!(abcd!!1 -1)) -(x!!(abcd!!0 -1)) == (abcd!!2) = (abcd!!3)
  |otherwise =0

scores x abcdq = sum [score x abcd | abcd <- abcdq]

--使用例
main = do
  nmq <- getInts
  abcdq <- getMat (nmq!!2)
  let x = [[z1,z2,z3,z4,z5,z6,z7,z8,z9,z0] | z1 <-[1..(nmq!!1)],z2 <-[z1..(nmq!!1)],z3 <-[z2..(nmq!!1)],z4 <-[z3..(nmq!!1)],z5 <-[z4..(nmq!!1)],z6 <-[z5..(nmq!!1)],z7 <-[z6..(nmq!!1)],z8 <-[z7..(nmq!!1)],z9 <-[z8..(nmq!!1)],z0 <-[z9..(nmq!!1)]]
  let y = maximum[scores z abcdq | z <- x]
  print y