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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (N, M, C) = readLine()!!.split(" ").map { it.toInt() }
    val Bn = readLine()!!.split(" ").map { it.toInt() }
    val An = (1..N).map { readLine()!!.split(" ").map { it.toInt() } }

    val ans = solve(Bn, An, C, M)
    println(ans)
}

fun solve(Bn: List<Int>, An: List<List<Int>>, C: Int, M: Int): String {
    val list = An.map { ai ->
        val result = (0 until M).map { ai[it] * Bn[it] }.sum() + C
        if (result > 0) {
            1
        } else {
            0
        }
    }
    return list.sum().toString()
}


/**
 * ファクション
 */
fun floor(target: Double): Double {
    return Math.floor(target)
}

fun ceil(target: Double): Double {
    return Math.ceil(target)
}