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++14 (GCC 5.4.1) (judge verdict: Accepted)

/*author: hyperion_1724
  date: 
*/
#include <bits/stdc++.h>
using namespace std;
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	// chrono::steady_clock sc;
 //  	auto start = sc.now();
 //  	ifstream cin;
 //  	cin.open("INPUT.txt");

	int N,M,C;
	cin>>N>>M>>C;
	int B[M];
	for (int i = 0; i < M; ++i)
	{
		cin>>B[i];
	}
	int ans=0;
	for (int i = 0; i < N; ++i)
	{
		int x=C;
		for (int i = 0; i < M; ++i)
		{
			int y;
			cin>>y;
			x+=y*B[i];
		}
		if(x>0)
		{
			ans++;
		}
	}
	cout<<ans<<endl;
	
	// cin.close();
	// auto end = sc.now();
 //   	auto time_span = static_cast<chrono::duration<double>>(end - start);
 //   	cout<<"Operation took: "<<time_span.count()<<" seconds";

	return 0;
}