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 Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner


object Main {

  def read() = {
    val sc = new Scanner(System.in)
    val nSamples, nFeatures, intercept = sc.nextInt()
    val coef: Seq[Int] = for (i <- 0 until nFeatures) yield sc.nextInt()
    val samples: Seq[Seq[Int]] = for (i <- 0 until nSamples) yield {
      for (j <- 0 until nFeatures) yield sc.nextInt()
    }
    (nSamples, nFeatures, intercept, coef, samples)
  }

  case class Classification(coef: Seq[Int], intercept: Int) {
    private def dot(x: Seq[Int], y: Seq[Int]): Int = (x, y).zipped.map(_ * _).sum

    def decisionFunction(x: Seq[Int]): Int = dot(x, coef) + intercept

    def predict(x: Seq[Int]): Boolean = decisionFunction(x) > 0
  }

  def solve(nSamples: Int, nFeatures: Int, intercept: Int, coef: Seq[Int], samples: Seq[Seq[Int]]): Int = {
    val clf = Classification(coef, intercept)
    val predicts = samples.map(clf.predict)
    predicts.count(p => p == true)
  }

  def main(args: Array[String]): Unit = {
    val (nSamples, nFeatures, intercept, coef, samples) = read()
    println(solve(nSamples, nFeatures, intercept, coef, samples))
  }
}