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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var NMC = ReadIntegersWithSpaces();
            int N = NMC[0];
            int M = NMC[1];
            int C = NMC[2];

            var BList = ReadIntegersWithSpaces();

            List<List<int>> AMatrix = new List<List<int>>();

            for(int k = 1; k <= N; k++)
            {
                AMatrix.Add(ReadIntegersWithSpaces());
            }

            int count = 0;
            int sum = 0;
            foreach(var row in AMatrix)
            {
                for(int k = 0; k <= M - 1; k++)
                {
                    sum += row[k] * BList[k];
                }
                sum += C;

                if(sum > 0)
                {
                    count++;
                }
            }

            Console.WriteLine(count);
        }


        public static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }

        public static List<int> ReadIntList(int length)
        {
            var list = new List<int>();
            for(int k = 1; k <= length; k++)
            {
                list.Add(ReadInt());
            }

            return list;
        }

        public static List<int> ReadIntegersWithSpaces()
        {
            var strings = Console.ReadLine().Split(' ');
            var integers = new List<int>();
            foreach(var str in strings)
            {
                integers.Add(int.Parse(str));
            }

            return integers;
        }

        public static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }

        public static List<long> ReadLongList(int length)
        {
            var list = new List<long>();
            for (int k = 1; k <= length; k++)
            {
                list.Add(ReadLong());
            }

            return list;
        }
    }
}