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.ComponentModel;
using System.Linq;
using System.Text;
using static System.Console;

namespace ABC121B
{
    static class Program
    {
        static void Main(string[] args)
        {
            var line = ReadLine().SplitTryParseToList<int>();
            var b = ReadLine().SplitTryParseToList<int>();
            var a = new List<List<int>>();
            for (int i = 0; i < line[0]; i++)
            {
                a.Add(ReadLine().SplitTryParseToList<int>());
            }

            var sum = new int[line[0]];
            for (int i = 0; i < line[0]; i++)
            {
                sum[i] = 0;
                for (int j = 0; j < line[1]; j++)
                {
                    sum[i] += (a[i][j] * b[j]);
                }
                sum[i] += line[2];
            }

            WriteLine(sum.Count(x => x > 0));

        }

        public static T TryParse<T>(this String input)
        {
            try
            {
                var converter = TypeDescriptor.GetConverter(typeof(T));
                if (converter != null)
                {
                    return (T)converter.ConvertFromString(input);
                }
                else
                {
                    throw new InvalidCastException("");
                }
            }
            catch
            {
                throw new InvalidCastException(typeof(T) + " is not supported.");
            }
        }

        public static List<T> SplitTryParseToList<T>(this String input)
        {
            return input.Split().Select(n => n.TryParse<T>()).ToList();
        }

        public static List<T> ListSwap<T>(this List<T> list, Int32 index1, Int32 index2)
        {
            var t = list[index1];
            list[index1] = list[index2];
            list[index2] = t;
            return list;
        }

        public static List<Tuple<T, int>> DuplicateCount<T>(this IEnumerable<T> list)
        {
            return list
                .GroupBy(i => i)
                .Where(g => g.Any())
                .Select(g => Tuple.Create(g.Key, g.Count()))
                .ToList();
        }
        public static List<Tuple<T, int>> DuplicateSort<T>(this IEnumerable<Tuple<T, int>> list)
        {
            return list.OrderByDescending((x) => x.Item2).ToList();
        }
        public static List<T> ReadLineOne<T>(int n)
        {
            var list = new List<T>();
            foreach (var i in Enumerable.Range(1, n))
            {
                list.Add(Console.ReadLine().TryParse<T>());
            }
            return list;
        }
        public static void PrintAll<T>(this IEnumerable<T> list)
        {
            foreach (var i in list)
            {
                Console.Write($"{i} ");
            }

            Console.WriteLine();
        }
    }
}