Uolevi is participating in a programming contest. There are $n$ tasks that have to be solved in order of difficulty. Task $i$ takes $m_i$ minutes to solve and solving it $t$ minutes after the contest started yields $p_i - t$ points. If task $i$ is harder than task $j$ then $m_i > m_j$. Uolevi can choose to skip some or all of the tasks. Skipping a task takes no time. What is the maximum number of points Uolevi can achieve?

Input

The first line contains a single integer $n$. The second line contains $n$ integers $m_1,\,m_2,\ldots,\,m_n$. The third line contains $n$ integers $p_1,\,p_2,\ldots,\,p_n$.

Output

Print the maximum score Uolevi can get.

Constraints

• $1 \le n \le 10^5$
• $1 \le m_i \le 10^6$
• $1 \le p_i \le 10^6$
• $m_i < m_j$ if $i < j$

Example 1

Input:

5
1 2 3 4 5 
10 19 19 12 14 

Output:

41

Example 2

Input:

10
3 5 8 9 11 13 16 17 18 20 
1 16 19 10 14 11 32 8 18 19

Output:

22