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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.io.InputStreamReader;
import java.io.BufferedReader;


class Main {
  public static void main(String[] args) throws Exception{
    
    //System.out.println("Hello Codiva");
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int N = Integer.parseInt(br.readLine());
    int M = Integer.parseInt(br.readLine());
    int C = Integer.parseInt(br.readLine());
    int arr[][] = new int[N][M];
    int arr2[] = new int [M];
    for(int j =0 ; j<M ;j++){
        arr2[j] = Integer.parseInt(br.readLine());
      }
    for(int i=0 ; i<N ; i++){
      
      for(int j =0 ; j<M ;j++){
        arr[i][j] = Integer.parseInt(br.readLine());
      }

    }
    int sum , count =0;
    for(int i=0 ; i<N ; i++){
      sum = 0 ;
      for(int j =0 ; j<M ;j++){
        sum+=arr[i][j]*arr2[j];
      }
      if(sum+C > 0){
        count++;
      }
    }
    
    System.out.println(count);
    
    
  }
}