It is the middle of 2018 and Maria Stepanovna, who lives outside Krasnokamensk (a town in Zabaikalsky region), wants to rent three displays to highlight an important problem.

There are $n$ displays placed along a road, and the $i$-th of them can display a text with font size $s_i$ only. Maria Stepanovna wants to rent such three displays with indices $i \lt j \lt k$ that the font size increases if you move along the road in a particular direction. Namely, the condition $s_i \lt s_j \lt s_k$ should be held.

The rent cost is for the $i$-th display is $c_i$. Please determine the smallest cost Maria Stepanovna should pay.

Input

The first line contains a single integer $n$ ($3 \le n \le 3\,000$) — the number of displays.

The second line contains $n$ integers $s_1, s_2, \ldots, s_n$ ($1 \le s_i \le 10^9$) — the font sizes on the displays in the order they stand along the road.

The third line contains $n$ integers $c_1, c_2, \ldots, c_n$ ($1 \le c_i \le 10^8$) — the rent costs for each display.

Output

If there are no three displays that satisfy the criteria, print -1. Otherwise print a single integer — the minimum total rent cost of three displays with indices $i \lt j \lt k$ such that $s_i \lt s_j \lt s_k$.

Note

In the first example you can, for example, choose displays $1$, $4$ and $5$, because $s_1 \lt s_4 \lt s_5$ ($2 \lt 4 \lt 10$), and the rent cost is $40 + 10 + 40 = 90$.

In the second example you can't select a valid triple of indices, so the answer is -1.