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.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;
class Program
{
    public static Scanner cin;
    static void Main()
    {
        
        cin = new Scanner();
        int[] nmc = cin.arrayInt(3);
        int[] bArray = cin.arrayInt(nmc[1]);
        int[][] aArray = new int[nmc[0]][];
        for(int a = 0; a < nmc[0]; a++)
        {
            aArray[a] = cin.arrayInt(nmc[1]);
        }
        int count = 0;
        
        for(int a = 0; a < nmc[0]; a++)
        {
            int total = 0;
            for(int b = 0; b < nmc[1]; b++)
            {
                total += bArray[b] * aArray[a][b];
            }
            total += nmc[2];
            if (total > 0) count++;
        }
        WriteLine(count);
        ReadLine();

    }
}





class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string input()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return input();
        i = 0;
        return s[i++];
    }

    public int inputInt()
    {
        return int.Parse(input());
    }
    public int[] arrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputInt() + add;
        }
        return Array;
    }

    public long inputLong()
    {
        return long.Parse(input());
    }

    public long[] arrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputLong() + add;
        }
        return Array;
    }

    public double inputDouble()
    {
        return double.Parse(input());
    }


    public double[] arrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = inputDouble() + add;
        }
        return Array;
    }
}