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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        int c = Integer.parseInt(sc.next());
        ArrayList<Integer> b_list = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            b_list.add(Integer.parseInt(sc.next()));
        }
        int ans = 0;
        for (int i = 0; i < n; i++) {
            int sum = 0;
            for (int j = 0, a = 0; j < m; j++) {
                a = Integer.parseInt(sc.next());
                sum += a * b_list.get(j);
            }
            sum += c;
            if (sum > 0) {
                ans++;
            }
        }
        out.println(ans);
        sc.close();
        out.close();
    }

}