Description

Tianyi has made a practice plan spanning $n$ days. She works extremely hard, and her daily practice duration must be monotonically non-decreasing. Meanwhile, to protect her voice, she can practice for a maximum of $t_i$ units of time on the $i$-th day. The effectiveness of practice varies from day to day, influenced by factors such as weather, and we quantify the effectiveness of practice on the $i$-th day as $w_i$, indicating that every unit of time she practices on that day will increase her familiarity by $w_i$. Note that it is possible for $w_i$ to be less than $0$, meaning that perhaps due to factors like excessive heat, her practice may have a negative impact.

Now, Tianyi has researched the weather forecast for the next $n$ days and estimated the values of $t_i$ and $w_i$ for each day. Please determine the maximum amount her familiarity can be improved.

Input Format

The first line of input contains an integer $n$ — the number of days in Tianyi's practice plan.

The second line of input contains $n$ integers $t_i$ — the maximum units of time Tianyi can spend on practicing on each day.

The third line of input contains $n$ integers $w_i$ — the effectiveness of practice on each day.

Output Format

The only line of output contains an integer — the maximum amount her familiarity can be improved.

3
3 2 3
2 -1 1

5

Hint

Sample Explanation

She practices for $2$ units of time on the first day,increasing her familarity by $4$;
She practices for $2$ units of time on the second day,increasing her familarity by $-2$ (decreasing by $2$);
She practices for $3$ units of time on the third day,increasing her familarity by $3$.
Tianyi's familiarity has increased by a total of 5.

It can be proved that there is no way to increase her familiarity higher than $5$.

Constraints

Subtasks Applied. You can only gain the score of the subtask if you accepted all the tests in the subtask.

Special Property: $t_i$ is uniformly randomly generated in $[0,10^9]$

For all tests, it is guaranteed that $1\le n\le10^6$，$0\le t_i\le10^9$，$-1000\le w_i\le1000$.