Tian Ji's Horse Racing

Problem Description

Corresponding multiple-choice / true-false questions: https://ti.luogu.com.cn/problemset/1136

You are going to race horses against Tian Ji. Each of you has $N$ horses, and you will compete in $N$ rounds; in each round both of you send out one horse to decide the winner.

Your horses' speeds are $u_1, u_2, \cdots, u_n$, and Tian Ji's horses' speeds are $v_1, v_2, \cdots, v_n$. Tian Ji sends his horses in order. How should you arrange your lineup to win the most rounds? By coincidence, all your and Tian Ji's horses have pairwise distinct speeds, so there can be no ties.

Input Format

The first line contains an integer $N$.

The second line contains $N$ integers $u_1, u_2, \cdots, u_n$, your horses' speeds.

The third line contains $N$ integers $v_1, v_2, \cdots, v_n$, Tian Ji's horses' speeds.

Output Format

Output one line containing one integer: the maximum number of rounds you can win.

Sample Input 1

3
1 3 5
2 4 6

Sample Input 2

5
10 3 5 8 7
4 6 1 2 9

Sample Output 1

2

Sample Output 2

5

Sample Explanation

Round 1: Tian Ji sends the horse of speed $2$; you can send the horse of speed $3$ to win this round.

Round 2: Tian Ji sends the horse of speed $4$; you can send the horse of speed $5$ to win this round.

Round 3: Tian Ji sends the horse of speed $6$; you send the horse of speed $1$, and Tian Ji wins this round.

Thus you win $2$ rounds.

Constraints

• $1\le N \le 5\times 10^4$;
• $1\le u_i, v_i \le 2N$;
• all horses' speeds are pairwise distinct; no ties occur.