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.

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.