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.Collections.Generic;

class Program
{
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split(' ');
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		int C = int.Parse(str[2]);

		string[] strB = Console.ReadLine().Split(' ');
		int[] B = new int[M];
		for (int i = 0; i < M; i++)
		{
			B[i] = int.Parse(strB[i]);
			// Console.WriteLine("Bは"+B[i]);
		}

		int[,] A = new int[N, M];
		for (int i = 0; i < N; i++)
		{
			string[] strA = Console.ReadLine().Split(' ');
			for (int j = 0; j < M; j++)
			{
				A[i, j] = int.Parse(strA[j]);
				// Console.WriteLine("Aは"+A[i,j]);
			}
		}
		//入力完了

		int fAns = 0;
		int[] ans = new int[N];
		for (int i = 0; i < N; i++)
		{
			for (int j = 0; j < M; j++)
			{
				ans[i] += A[i,j] * B[j];
			}
			ans[i] += C;
			// Console.WriteLine(ans[i]);
			if(ans[i] > 0)
				fAns++;
		}
		Console.WriteLine(fAns);
	}
}