Problem:
Score : 200 points

Problem Statement

There are N pieces of source code. The characteristics of the i-th code is represented by M integers A_{i1}, A_{i2}, ..., A_{iM}.

Additionally, you are given integers B_1, B_2, ..., B_M and C.

The i-th code correctly solves this problem if and only if A_{i1} B_1 + A_{i2} B_2 + ... + A_{iM} B_M + C > 0.

Among the N codes, find the number of codes that correctly solve this problem.

Constraints

All values in input are integers.

1 \leq N, M \leq 20

-100 \leq A_{ij} \leq 100

-100 \leq B_i \leq 100

-100 \leq C \leq 100

Input

Input is given from Standard Input in the following format:

N M C
B_1 B_2 ... B_M
A_{11} A_{12} ... A_{1M}
A_{21} A_{22} ... A_{2M}
\vdots
A_{N1} A_{N2} ... A_{NM}

Output

Print the number of codes among the given N codes that correctly solve this problem.

Sample Input 1

2 3 -10
1 2 3
3 2 1
1 2 2

Sample Output 1

1

Only the second code correctly solves this problem, as follows:

Since 3 \times 1 + 2 \times 2 + 1 \times 3 + (-10) = 0 \leq 0, the first code does not solve this problem.

1 \times 1 + 2 \times 2 + 2 \times 3 + (-10) = 1 > 0, the second code solves this problem.

Sample Input 2

5 2 -4
-2 5
100 41
100 40
-3 0
-6 -2
18 -13

Sample Output 2

2

Sample Input 3

3 3 0
100 -100 0
0 100 100
100 100 100
-100 100 100

Sample Output 3

0

All of them are Wrong Answer. Except yours.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)


import qualified Data.Vector.Unboxed as V
import Data.Array.IArray (listArray, accumArray, (!))
import Data.Array.MArray
import Data.Array.ST (STUArray, runSTUArray)
import Data.Array.Unboxed (UArray)
import Data.List (sortOn, sortBy, unfoldr, partition)
import Data.Char (isSpace)
import Control.Monad.ST (ST)
import Control.Monad.Trans.State (StateT(..))
import qualified Data.ByteString.Char8 as B

-- utility functions

--   Input functions
readInt = B.readInt . B.dropWhile isSpace

readInts :: Int -> B.ByteString -> [Int]
readInts n = take n . unfoldr readInt

readIntsV :: Int -> B.ByteString -> V.Vector Int
readIntsV n = V.unfoldrN n readInt

readIntsA :: Int -> B.ByteString -> UArray Int Int
readIntsA n bs = runSTUArray $ do
  arr <- newArray_ (0,n-1)
  go arr 0 bs
  return arr
  where
    go :: STUArray s Int Int -> Int -> B.ByteString -> ST s ()
    go arr i bs
      | i==n = return ()
      | otherwise = do
        let Just (x,bs') = readInt bs
        writeArray arr i x
        go arr (i+1) bs'

readTsV :: Int -> B.ByteString -> V.Vector (Int,Int)
readTsV n = V.unfoldrN n $ runStateT ((,) <$> StateT readInt <*> StateT readInt)

readTs :: Int -> B.ByteString -> [(Int,Int)]
readTs n = take n . unfoldr readT where
  readT = runStateT ((,) <$> StateT readInt <*> StateT readInt)

-- main

solv bs ass c = length $ filter id [f as | as <- ass] where
  f as = sum (zipWith (*) as bs) + c > 0

main = do
  [n,m,c] <- map read . words <$> getLine
  bs <- readInts m <$> B.getLine
  ass <- map (readInts m) . B.lines <$> B.getContents
  print $ solv bs ass c