Ball momentum

There are $n$ baseball balls and $n$ machines for serving them. Each ball has its weight $w_i$ and each machine has its power of serving $p_i$. We can choose a ball and machine to serve it. Let's say that difficulty of catching $i$-th ball served using machine $j$ is $w_i\times p_j$. You want to pick a pair ($i;j$) such that any other pair ($i^{\prime };j^{\prime }$) ($i\ne i^{\prime }$ and $j\ne j^{\prime }$) has difficulty of catching less or equal to the difficulty of catching the pair($i;j$). Tell the number of such pairs.

Input

The first line of input contains a single integer $n$ ($1\le n\le 2\cdot 10^5$) — number of balls and serving machines.

The second line of input contains $n$ integers $w_i$ ($1\le w_i\le 10^9$) — weitghts of balls.

The third line of input contains $n$ integers $p_i$ ($1\le p_i\le 10^9$) — powers of serving machines.

Output

Print one integer — answer to the problem.

Examples

Scoring

1. ($7$ points): $n\le 3$;

2. ($7$ points): all $w_i$ are equal and all $p_i$ are equal;

3. ($8$ points): all $w_i$ are equal;

4. ($9$ points): $w_i,p_i\le 1000$;

5. ($23$ points): $n\le 100$

6. ($24$ points): $n\le 1000$

7. ($22$ points): no additional restrictions.