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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Collections;
public class Program {
  public static void Main() {
    int[] NMC = ReadIntArray();
    int[] B = ReadIntArray();
    int res = 0;
    for (int i = 0; i < NMC[0]; i++) {
      int[] A = ReadIntArray();
      int temp = 0;
      for (int j = 0; j < NMC[1]; j++) {
        temp += A[j] * B[j];
      }
      temp += NMC[2];
      if (temp > 0) {
        res++;
      }
    }
    Console.WriteLine(res);
  }

  private static string ReadStr() { return Console.ReadLine(); }
  private static int ReadInt() { return int.Parse(Console.ReadLine()); }
  private static double ReadDouble() { return double.Parse(Console.ReadLine()); }
  private static long ReadLong() { return long.Parse(Console.ReadLine()); }
  private static char ReadChar() { return Console.ReadLine()[0]; }
  private static string[] ReadStringArray() { return Console.ReadLine().Split(' '); }
  private static int[] ReadIntArray() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
  private static double[] ReadDoubleArray() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
  private static long[] ReadLongArray() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
  private static char[] ReadCharArray() { return Console.ReadLine().ToArray(); }
  private static string[] ReadCharStringArray() { return Console.ReadLine().ToCharArray().Select(c => c.ToString()).ToArray(); }
}