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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

package test;

import java.util.Scanner;
public class Main{
	
	public static void main (String[] args) {
		
		Main main = new Main();
		main.solve();
	}
	
	private void solve() {
		
		Scanner scanner = new Scanner (System.in);
		
		int N = scanner.nextInt();
		int M = scanner.nextInt();
		int C = scanner.nextInt();
		
		int[] list = new int [M];
		
		for (int index=0; index<M; index++) {
			list[index]=scanner.nextInt();
		}
		
		int count = 0;
		
		for (int index=0; index<N; index++) {
			int sum = 0;
			for (int index2=0; index2<M; index2++) {
				int number = scanner.nextInt();
				sum+=(number*list[index2]);
			}
			
			sum+=C;
			
			if (sum>0) {
				count++;
			}
			
		}
		
		System.out.println(count);
	}
}