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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php /*atcoder.php*/

$at = new Atcoder();
$at->main();
unset($at);

class Atcoder{
	private function arrayIn(){
		$buf = explode(" ", fgets(STDIN));
		return $this->killNewLine($buf);
	}
	private function killNewLine($buf = null){
		$buf = str_replace("\r\n", "", $buf);
		$buf = str_replace("\n", "", $buf);
		$buf = str_replace("\r", "", $buf);
		return $buf;
	}

	public function main(){
		$s = $this->arrayIn();
		
		$n = $s[0];
		$m = $s[1];
		$c = $s[2];

		$i = array();

		$i = $this->arrayIn();

		$ans = 0;
		$buf = 0;
		$j = array();
		for($k = 0; $k < $n; $k++){
			$j = $this->arrayIn();
			for($ii = 0; $ii < $m; $ii++){
				$buf += ($i[$ii] * $j[$ii]);
			}
			$buf += $c;
			if(0 < $buf){
				$ans++;
			}
			$buf = 0;
		}

		echo $ans . "\n";

	}
}
?>