Score : $800$ points

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.
• 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.

Constraints

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

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.

3
1 2 3
1 2 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.

4
1 3 5 7
3 1 4 1

0