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;

class Program
{
    static void Main(string[] args)
    {
        var constants = ReadInts();
        var N = constants[0];
        var M = constants[1];
        var C = constants[2];

        var B = ReadInts();

        var ans = 0;

        for(var i = 0; i < N; i++)
        {
            var A = ReadInts();

            if (A.Select((a, idx) => a * B[idx]).Sum() + C > 0) ans++;
        }

        Console.WriteLine(ans);
    }

    public static string Read() { return Console.ReadLine(); }
    public static int ReadInt() { return int.Parse(Read()); }
    public static long ReadLong() { return long.Parse(Read()); }
    public static double ReadDouble() { return double.Parse(Read()); }

    public static string[] Reads() { return Console.ReadLine().Split(' '); }
    public static int[] ReadInts() { return Reads().Select(_ => int.Parse(_)).ToArray(); }
    public static long[] ReadLongs() { return Reads().Select(_ => long.Parse(_)).ToArray(); }
    public static double[] ReadDoubles() { return Reads().Select(_ => double.Parse(_)).ToArray(); }
}