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;
using static ABC121B.Input;

namespace ABC121B
{
    class Input
    {
        /// <summary>
        /// 1行の文字列の入力
        /// </summary>
        public static void @in(out string s)
        {
            s = String();
        }

        private static String String()
        {
            return Console.ReadLine();
        }

        /// <summary>
        /// 複数行の文字列の入力
        /// </summary>
        public static void @in(long rowNumber, out string[] s)
        {
            s = new String[rowNumber];
            for (long i = 0; i < rowNumber; i++) @in(out s[i]);
        }

        /// <summary>
        /// 1行に書かれた1つの整数の入力
        /// </summary>
        public static void @in(out int i)
        {
            i = int.Parse(String());
        }

        /// <summary>
        /// 1行に書かれた1つの整数の入力
        /// </summary>
        public static void @in(out long a)
        {
            a = Long()[0];
        }

        /// <summary>
        /// 1行に書かれた2つの整数の入力
        /// </summary>
        public static void @in(out long a, out long b)
        {
            long[] lArr = Long();
            a = lArr[0];
            b = lArr[1];
        }

        /// <summary>
        /// 1行に書かれた3つの整数の入力
        /// </summary>
        public static void @in(out long a, out long b, out long c)
        {
            long[] lArr = Long();
            a = lArr[0];
            b = lArr[1];
            c = lArr[2];
        }

        /// <summary>
        /// 1行に書かれた4つの整数の入力
        /// </summary>
        public static void @in(out long a, out long b, out long c, out long d)
        {
            long[] lArr = Long();
            a = lArr[0];
            b = lArr[1];
            c = lArr[2];
            d = lArr[3];
        }

        /// <summary>
        /// 1行に書かれた5つの整数の入力
        /// </summary>
        public static void @in(out long a, out long b, out long c, out long d, out long e)
        {
            long[] lArr = Long();
            a = lArr[0];
            b = lArr[1];
            c = lArr[2];
            d = lArr[3];
            e = lArr[4];
        }

        private static long[] Long()
        {
            return Split().Select(long.Parse).ToArray();
        }

        /// <summary>
        /// 1行に書かれた複数の整数列の入力
        /// </summary>
        public static void @in(out long[] lArr)
        {
            lArr = Long();
        }

        /// <summary>
        /// rowNumber行に書かれた1つの整数列の入力
        /// </summary>
        public static void @in(long rowNumber, out long[] lArr)
        {
            lArr = new long[rowNumber];
            for (long i = 0; i < rowNumber; i++) @in(out lArr[i]);
        }

        /// <summary>
        /// rowNumber行に書かれた2つの整数列の入力
        /// </summary>
        public static void @in(long rowNumber, out long[] a, out long[] b)
        {
            a = new long[rowNumber];
            b = new long[rowNumber];
            for (int i = 0; i < rowNumber; i++) @in(out a[i], out b[i]);
        }

        /// <summary>
        /// rowNumber行に書かれた3つの整数列の入力
        /// </summary>
        public static void @in(long rowNumber, out long[] a, out long[] b, out long[] c)
        {
            a = new long[rowNumber];
            b = new long[rowNumber];
            c = new long[rowNumber];
            for (int i = 0; i < rowNumber; i++) @in(out a[i], out b[i], out c[i]);
        }

        /// <summary>
        /// rowNumber行に書かれた4つの整数列の入力
        /// </summary>
        public static void @in(long rowNumber, out long[] a, out long[] b, out long[] c, out long[] d)
        {
            a = new long[rowNumber];
            b = new long[rowNumber];
            c = new long[rowNumber];
            d = new long[rowNumber];
            for (int i = 0; i < rowNumber; i++) @in(out a[i], out b[i], out c[i], out d[i]);
        }

        /// <summary>
        /// h行w列の整数の行列の入力
        /// </summary>
        public static void @in(long h, long w, out long[][] a)
        {
            a = new long[h][];
            for (long i = 0; i < h; i++) @in(out a[i]);
        }

        /// <summary>
        /// 1行に書かれた1つの小数の入力
        /// </summary>
        public static void @in(out double d)
        {
            d = double.Parse(String());
        }

        /// <summary>
        /// 1行に書かれた小数の配列の入力
        /// </summary>
        public static void @in(out double[] dArr)
        {
            dArr = Split().Select(double.Parse).ToArray();
        }

        private static IEnumerable<string> Split()
        {
            return String().Split(' ');
        }
    }

    class Program
    {
        public static void Main(string[] args)
        {
            StreamWriter streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            new Solver().Solve();
            Console.Out.Flush();
        }

        public static void Debug()
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        private long N;
        private long M;
        private long C;
        private long[] B;
        private long[][] A;

        public void Solve()
        {
            @in(out N, out M, out C);
            @in(out B);
            @in(N, M, out A);

            int ans = 0;
            for (int i = 0; i < N; i++)
            {
                var a = C;
                for (int j = 0; j < M; j++)
                {
                    a += A[i][j] * B[j];
                }

                if (a > 0) ans++;
            }

            Console.WriteLine(ans);
        }
    }
}