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;
using System.Linq;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("2 3 -10");
            WillReturn.Add("1 2 3");
            WillReturn.Add("3 2 1");
            WillReturn.Add("1 2 2");
            //1
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("5 2 -4");
            WillReturn.Add("-2 5");
            WillReturn.Add("100 41");
            WillReturn.Add("100 40");
            WillReturn.Add("-3 0");
            WillReturn.Add("-6 -2");
            WillReturn.Add("18 -13");
            //2
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("3 3 0");
            WillReturn.Add("100 -100 0");
            WillReturn.Add("0 100 100");
            WillReturn.Add("100 100 100");
            WillReturn.Add("-100 100 100");
            //0
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();

        SplitAct(InputList[0]);
        int C = wkArr[2];

        SplitAct(InputList[1]);
        int[] BArr = wkArr;

        var AArrList = new List<int[]>();
        foreach (string EachStr in InputList.Skip(2)) {
            SplitAct(EachStr);
            AArrList.Add(wkArr);
        }

        int AnswerCnt = 0;
        foreach (int[] EachAArr in AArrList) {
            int ProdSum = 0;
            for (int I = 0; I <= BArr.GetUpperBound(0); I++) {
                ProdSum += BArr[I] * EachAArr[I];
            }
            if (ProdSum + C > 0) AnswerCnt++;
        }
        Console.WriteLine(AnswerCnt);
    }
}