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.Numerics;
using System.Linq;

namespace AtCoderTemplate
{
    class Program
    {
        static void Main(string[] args)
        {
            var c = Scanner.scanint;
            var b = Scanner.scanint;
            var a = Scanner.rescanint(c[0]);

            var res = 0;
            for(var i = 0; i < c[0]; i++)
            {
                var sum = 0;
                for(var j = 0; j < c[1]; j++)
                {
                    sum += a[i][j] * b[j];
                }
                sum += c[2];
                if (sum > 0) res++;
            }
            Console.WriteLine(res);
        }
    }

    public class Scanner
    {
        public static string[] scan => Console.ReadLine().Split(' ');
        public static int[] scanint => Array.ConvertAll(scan, int.Parse);
        public static long[] scanlong => Array.ConvertAll(scan, long.Parse);
        public static string[][] rescan(int n) => Enumerable.Repeat(0, n).Select(_ => scan).ToArray();
        public static int[][] rescanint(int n) => Enumerable.Repeat(0, n).Select(_ => scanint).ToArray();
        public static long[][] rescanlong(int n) => Enumerable.Repeat(0, n).Select(_ => scanlong).ToArray();

    }

    public class Ex
    {
        public static int[] subarr(int[] arr, int begin, int n) { int[] a = new int[arr.Length]; Array.Copy(arr, begin, a, 0, n); return a; }
    }
}