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.Linq;
using System.Runtime.Remoting;
using System.Security.Cryptography;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = ReadLineIntSpilit();
            var b = ReadLineIntSpilit();
            var a = new int[n[0]][];
            for (int i = 0; i < n[0]; i++) {
                a[i] = ReadLineIntSpilit();
            }

            var count = 0;

            for (int i = 0; i < n[0]; i++) {
                var total = 0;
                for (int j = 0; j < n[1]; j++) {
                    total += a[i][j] * b[j];
                }
                if (total + n[2] > 0) count++;
            }

            Console.WriteLine(count);
            ReadLine();
        }

        //メモ

        //アルゴリズム

        //・全探索解

        /*
         * 例 [A, B, C]
         *
         *  A - B, A - C
         *  B - C
         * 
         *   for (int i = 0; i < n; i++) {
         *  
         *       for (int j = i + 1; j < n; j++) {
         *
         *           array[i], array[j]
         *
         *       }
         *   }
         */

        // ・配列の前後を見る

        /*
         *  例 array[1, 2, 3, 4, 5]
         *  
         *  r = 3;
         * 
         *  array[i - 1] => 1
         *  array[i] => 2
         *  array[i + 1] => 3
         * 
         * //範囲
         * int r = 3;
         * 
         * for(int i = 1; i <= array.Length - r; i++) { }
         * 
         */

        //配列 --------------------

        //降順
        //Array.Sort(h);
        //Array.Reverse(h);

        //合計値
        //array.Sum();

        //最大値
        //List.Sort(); List[Count() - 1] 

        //連続の整数配列を作成
        //
        // 1, 2, 3, 4, 5,..., n
        //var continuous = Enumerable.Range(1, n).ToList();

        //--------------------

        //切り捨て

        //double d = Math.Floor(n);

        //切り上げ

        //double d = Math.Celling(n);

        //kのn乗
        //(int) Math.Pow(k, n);

        //for文の逆
        //for(int i = array.Length - 1; i >= 0; i--) { }


        /// <summary>
        /// 最大公約数
        /// </summary>
        public static long Gcd(long a, long b)
        {
            while (true) {
                if (a < b) { long tmp = b; b = a; a = tmp; }
                if (a % b == 0) return b;
                var x = a;
                a = b;
                b = x % b;
            }
        }

        /// <summary>
        /// 最小公倍数
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public static long Lcm(long a, long b) => a / Gcd(a, b) * b;

        /// <summary>
        /// コンビネーション
        /// </summary>
        static int nCm(int n, int m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * nCm(n - 1, m - 1) / m;
        }

        /// <summary>
        /// 数字配列の重複をカウント
        /// </summary>
        public static int DistinctInt(IEnumerable<int> array)
        {
            var q = array.Distinct().Count();
            return array.Count() - q;
        }

        /// <summary>
        /// 文字配列の重複をカウント
        /// </summary>
        /// <param name="array"></param>
        /// <returns></returns>
        public static int DistinctString(IEnumerable<string> array)
        {
            var q = array.Distinct().Count();
            return array.Count() - q;
        }

        public static string ReadLine() => Console.ReadLine();
        public static int ReadLineInt() => int.Parse(Console.ReadLine());
        public static long ReadLineLongInt() => long.Parse(Console.ReadLine());
        public static string[] ReadLineStringSplit(char a = ' ') => ReadLine().Split(a).ToArray();
        public static int[] ReadLineIntSpilit(char a = ' ') => ReadLine().Split(a).Select(x => int.Parse(x)).ToArray();
        public static long[] ReadLineLongSpilit(char a = ' ') => ReadLine().Split(a).Select(x => long.Parse(x)).ToArray();
        static string[] GetAlphaLowerArray() => new string[] { "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z" };
        static string[] GetAlphaUpperArray() => new string[] { "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z" };
    }
}