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.Diagnostics;
using System.IO;

namespace AtCoder.ABC121 {
    class B {
        static void Main() => CustomMain();

        static void Solve() {
            int n, m, c;
            ReadMulti(out n, out m, out c);
            var b = ReadIntArray();
            var ans = 0;
            for (int i = 0; i < n; i++) {
                var a = ReadIntArray();
                var total = 0;
                for (int j = 0; j < m; j++) {
                    total += a[j] * b[j];
                }

                total += c;
                if (total > 0) {
                    ans++;
                }
            }

            WriteAnswer(ans);
        }

        static void CustomMain() {
#if DEBUG
            // ファイルからテストケースを読み込む
            global::Common.ChangeStdIn();
            // 時間計測
            var stopwatch = new Stopwatch();
            stopwatch.Start();
#endif
            // 出力高速化
            var streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            // 回答
            Solve();
#if DEBUG
            stopwatch.Stop();
            Console.WriteLine(stopwatch.Elapsed);
#endif
            Console.Out.Flush();
        }

        static string ReadString() => Console.ReadLine().Trim();
        static int ReadInt() => int.Parse(ReadString());
        static long ReadLong() => long.Parse(ReadString());
        static float ReadFloat() => float.Parse(ReadString());
        static double ReadDouble => double.Parse(ReadString());

        static string[] ReadStringArray() => ReadString().Split(' ');
        static int[] ReadIntArray() => Array.ConvertAll(ReadString().Split(' '), int.Parse);
        static long[] ReadLongArray() => Array.ConvertAll(ReadString().Split(' '), long.Parse);
        static float[] ReadFloatArray() => Array.ConvertAll(ReadString().Split(' '), float.Parse);
        static double[] ReadDoubleArray() => Array.ConvertAll(ReadString().Split(' '), double.Parse);

        static T TypeConversion<T>(string s) {
            if (typeof(T) == typeof(int)) {
                return (T) Convert.ChangeType(int.Parse(s), typeof(T));
            } else if (typeof(T) == typeof(long)) {
                return (T) Convert.ChangeType(long.Parse(s), typeof(T));
            } else if (typeof(T) == typeof(double)) {
                return (T) Convert.ChangeType(double.Parse(s), typeof(T));
            } else {
                return (T) Convert.ChangeType(s, typeof(T));
            }
        }

        static void ReadMulti<T, U>(out T a, out U b) {
            var str = ReadStringArray();
            a = TypeConversion<T>(str[0]);
            b = TypeConversion<U>(str[1]);
        }

        static void ReadMulti<T, U, V>(out T a, out U b, out V c) {
            var str = ReadStringArray();
            a = TypeConversion<T>(str[0]);
            b = TypeConversion<U>(str[1]);
            c = TypeConversion<V>(str[2]);
        }

        static void WriteAnswer(object ans) => Console.WriteLine(ans);

        static bool IsOdd(long num) {
            return (num & 1) == 1;
        }

        static bool IsEven(long num) {
            return (num & 1) == 0;
        }
    }
}