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;

// AtCorder用のTemplate
namespace Atcoder{
    public class main{

        // 標準入力用汎用関数
        static string readString(){return Console.ReadLine();}
        static int readInteger(){return int.Parse(Console.ReadLine());}
        static long readLong(){return long.Parse(Console.ReadLine());}
        static double readDouble(){return double.Parse(Console.ReadLine());}
        static decimal readDecimal(){return decimal.Parse(Console.ReadLine());}

        static List<char> readCharL(char separator=' '){return Console.ReadLine().Split(separator).Select((x) => Convert.ToChar(x)).ToList();}
        static List<string> readStringL(char separator=' '){return Console.ReadLine().Split(separator).ToList();}
        static List<int> readIntegerL(char separator=' '){return Console.ReadLine().Split(separator).Select((x) => int.Parse(x)).ToList();}

        static void print<T>(T args){Console.WriteLine(args);}
        static void printL<T>(List<T> _list){Console.WriteLine(string.Join(",", _list));}

        public static void Main(string[] args)
        {
            var tmp = readIntegerL();
            int N = tmp[0];
            int M = tmp[1];
            int C = tmp[2];
            var B = readIntegerL();

            int counter = 0;

            foreach(var i in Enumerable.Range(0, N))
            {
                var sum = 0;
                var _list = readIntegerL();
                for(var j = 0; B.Count() > j; j++)
                {
                    var tmp2 = _list[j] * B[j];
                    sum += tmp2;
                }
                if((sum + C) > 0)
                {
                    counter++;
                }
            }
            Console.WriteLine(counter);
        }
    }
}