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.IO;
using System.Linq;

namespace ABC121B
{
    public partial class Program
    {
        void Solve(StreamScanner ss, StreamWriter sw)
        {
            //---------------------------------
            var N = ss.Next(int.Parse);
            var M = ss.Next(int.Parse);
            var C = ss.Next(int.Parse);

            var B = ss.Next(int.Parse, M);
            var A = ss.Next(int.Parse, M, N);

            var ans = 0;

            for (var i = 0; i < N; i++)
            {
                var calc = C;

                for (var j = 0; j < M; j++)
                {
                    var a = A[i][j];
                    var b = B[j];
                    calc += a * b;
                }

                if (calc > 0) ans++;
            }

            sw.WriteLine(ans);
            //---------------------------------
        }
    }

    public class StreamScanner
    {
        static readonly char[] Separator = { ' ' };
        readonly StreamReader streamReader;

        string[] line = new string[0];
        int index = 0;

        public StreamScanner(Stream stream)
        {
            this.streamReader = new StreamReader(stream);
        }

        public string Next()
        {
            return Next(s => s);
        }

        public string[] Next(int x)
        {
            return Next(s => s, x);
        }

        public string[][] Next(int x, int y)
        {
            return Next(s => s, x, y);
        }

        public T Next<T>(Func<string, T> parser)
        {
            if (index < line.Length) return parser(line[index++]);
            index = 0;
            line = streamReader.ReadLine()?.Split(Separator, StringSplitOptions.RemoveEmptyEntries);
            return Next(parser);
        }

        public T[] Next<T>(Func<string, T> parser, int x)
        {
            var ret = new T[x];
            for (var i = 0; i < x; ++i) ret[i] = Next(parser);
            return ret;
        }

        public T[][] Next<T>(Func<string, T> parser, int x, int y)
        {
            var ret = new T[y][];
            for (var i = 0; i < y; ++i) ret[i] = Next(parser, x);
            return ret;
        }
    }

    public partial class Program
    {
        static void Main()
        {
            Excute(Console.OpenStandardInput(), Console.OpenStandardOutput());
        }

        public static void Excute(Stream input, Stream output)
        {
            var ss = new StreamScanner(input);
            var sw = new StreamWriter(output);
            new Program().Solve(ss, sw);
            sw.Flush();
        }
    }
}