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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

namespace b
{
    class Program
    {
        static void Main(string[] args)
        {
            var (n, m, c, xs) = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            var bseq = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var ans = 0;

            for (var i = 0; i < n; ++i) {
                var aseq = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

                var correct = bseq.Zip(aseq, (b, a) => b * a).Sum() + c;
                if (correct > 0) ++ans;
            }
            Console.WriteLine(ans);
        }
    }

    public static class ArrayDeconstruct {
        public static void Deconstruct<T>(this T[] source, out T d1, out T d2, out T d3, out T[] rest) {
            const int maxLen = 3;
            var len = source.Length;

            d1 = default;
            d2 = default;
            d3 = default;

            if (len > 0) d1 = source[0];
            if (len > 1) d2 = source[1];
            if (len > 2) d3 = source[2];

            rest = source.Skip(maxLen).ToArray();
        }
    }
}