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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder.ABC113.D
{
    class Program
    {
        static void Main()
        {
            var sc = new Scanner();
            var N = sc.Nextint();
            var M = sc.Nextint();
            var C = sc.Nextint();
            var B = sc.Arrayint(M);
            var A = Enumerable.Range(0, N)
                .Select(_ => sc.Arrayint(M))
                .ToArray();

            var correctCount = A.Select(Ai => Enumerable.Range(0, M).Aggregate(0,
                    (sum, j) => sum += Ai[j] * B[j],
                    sum => sum + C))
                .Where(val => val > 0)
                .Count();
            Console.WriteLine(correctCount);
        }
    }

    class Scanner
    {
        string[] s;
        long i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string Next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return Next();
            i = 0;
            return s[i++];
        }

        public int Nextint()
        {
            return int.Parse(Next());
        }
        public int[] Arrayint(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Nextint() + add;
            }
            return Array;
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (long i = 0; i < N; i++)
            {
                Array[i] = NextLong() + add;
            }
            return Array;
        }

        public double NextDouble()
        {
            return double.Parse(Next());
        }

        public double[] ArrayDouble(long N, double add = 0)
        {
            double[] Array = new double[N];
            for (long i = 0; i < N; i++)
            {
                Array[i] = NextDouble() + add;
            }
            return Array;
        }

        public decimal NextDecimal()
        {
            return decimal.Parse(Next());
        }

        public decimal[] ArrayDecimal(long N, decimal add = 0)
        {
            decimal[] Array = new decimal[N];
            for (long i = 0; i < N; i++)
            {
                Array[i] = NextDecimal();
            }
            return Array;
        }
    }
}