Problem Statement

There are robots on a number line.
Specifically, for each $i=0,1,2,\cdots,10^{100},$ there is exactly one robot called Robot i at coordinate i.
We have many balls.
Each of the balls has a positive integer written on it.
Integer sequences A and B, each of length N, describe these balls.
Specifically, for each $i (1 \leq i \leq N),$ there are B_i balls with A_i written on them.
Now, Snuke will do the following sequence of operations:

• Step 1: Choose zero or more balls and replace the integers written on those balls with positive integers of his choice between 1 and 10^{100} (inclusive). (The new integers can be chosen independently from each other.)

• Step 2: Eat the balls one by one in any order of his choice. Each time he eats a ball, he should do the following:

• Let v be the integer written on the ball he has just eaten. If Robot v exists, move it so that its coordinate decreases by 1. Here, if there is another robot at the destination, that robot (not Robot v) will be destroyed.

Snuke wants to eat all the balls without destroying Robot 0.
Find the minimum number of balls Snuke must choose in Step 1 to achieve his objective.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$
$B_1 B_2 \ldots B_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_1 < A_2 < \ldots < A_N \leq 10^9$
• $1 \leq B_i \leq 10^9$

Sample Input 1

3
1 2 3
1 2 1

Sample Output 1

1

We can achieve the objective by choosing one ball with 2 written on it, rewriting 3 on it, and then eating the balls in the following order:

• Eat the ball with 2 written on it, moving Robot 2 from coordinate 2 to coordinate 1 and destroying Robot 1.

• Eat the ball with 3 written on it, moving Robot 3 from coordinate 3 to coordinate 2.

• Eat the ball with 3 written on it, moving Robot 3 from coordinate 2 to coordinate 1 and destroying Robot 2.

• Eat the ball with 1 written on it. Robot 1 is already destroyed, so nothing happens.

Sample Input 2

4
1 3 5 7
3 1 4 1

Sample Output 2

0

见题面 Input 部分

见题面 Output 部分