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 void Main(string[] args)
    {
        // 解
        int ans = 0;

        // 入力
        int[] inp1 = CSRD.RI(' ');  //SC数：N, SCを構成する整数Aの数：M, 整数：C
        int n = inp1[0];
        int m = inp1[1];
        int c = inp1[2];
        int[] barr = CSRD.RI(' ');  //整数：B(M個分)
        int[][] aarr = new int[20][];
        for (int i = 0; i < n; i++)
        {
            aarr[i] = CSRD.RI(' ');  //整数：A(N * M個分)
        }
        
        // 処理
        for (int i = 0; i < n; i++)
        {
            int scAns = 0;
            for (int j = 0; j < aarr[i].Length; j++)
            {
                scAns = scAns + (aarr[i][j] * barr[j]);
            }
            scAns = scAns + c;
            if (scAns > 0)
            {
                ans++;
            }
        }
        


        //出力
        CSWT.WS(ans);
    }
}

class CSRD
{
    // 文字列または数値の入力
    public static string RS() { return Console.ReadLine(); }
    public static int RI() { return int.Parse(Console.ReadLine()); }
    public static string[] RS(char sep) { return Console.ReadLine().Split(sep); }
    public static int[] RI(char sep) { return Console.ReadLine().Split(sep).Select(x => int.Parse(x)).ToArray(); }
}

class CSWT
{
    public static void WS(object param) { Console.WriteLine(param); }
}