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(String::toInt)
	val N : Int = n.toInt()
	val M : Int = m.toInt()
	val C : Int = c.toInt()
	val list1 = readLine()!!.split(" ").map(String::toInt)
	var bList : MutableList<Int> = mutableListOf()
	for (i in 0..M - 1) {
		bList.add(list1[i])
	}
	var aList : MutableList<Int> = mutableListOf()
	var calc : Int = 0
	var count : Int = 0
	for (i in 0..N - 1) {
		var list2 = readLine()!!.split(" ").map(String::toInt)
		for (j in 0..M - 1) {
			aList.add(list2[j])
			calc += (bList[j] * aList[j])
		}
		calc += C
		if (calc > 0) {
			count++
		}
		calc = 0
		aList.clear()
	}
	println("${count}")
}