Problem Description

There are $n$ objects. For the $i$ -th object, its value is $s_i$ , and you may choose any real number $v_i$ such that $x_i \le v_i \le y_i$ . Define the score of the $i$ -th object as $\frac{s_i}{v_i}$ .

An object is called good if there exists a choice of values $v_1, v_2 , \ldots , v_n$ such that its score is not greater than the score of any other object. If several objects have the same minimum score, all of them are considered good. Find the number of good objects.

Input Format

The first line contains an integer $n$ $(1 \le n \le 10^5 )$ .

The second line contains $n$ integers $s_1 , s_2 , \ldots, s_n$ .

The third line contains $n$ integers $x_1 , x_2 , \ldots , x_n$ .

The fourth line contains $n$ integers $y_1 , y_2 , \ldots , y_n$ .

It is guaranteed that $x_i \le y_i$ for each $1 \le i \le n$ .

Output Format

Print the number of good objects.

Examples

Example 1

Input

4
15 10 50 100
2 3 1 20
7 4 1 50

Output

Explanation

In the first sample, the first, second, and fourth objects are good, while the third one is not.

Example 2