Problem Statement

There are buttons numbered from $1$ to $N$ and a sequence $A$ of positive integers of length $N$.
Button $i$ is located at coordinate $X_i$ on a number line, and pressing button $i$ $1$ time decreases $A_i$ by $1$.
However, the same button cannot be pressed consecutively. More precisely, when buttons $B_1,B_2,\dots,B_K$ are pressed in this order, $B_j\neq B_{j+1}$ must hold for every $j$ satisfying $1\le j\le K-1$.
Determine whether it is possible to make all elements of $A$ equal to $0$, and if it is possible, find the minimum distance traveled on the number line from the first button press to the last button press.

Constraints

• All inputs are integers.
• $1\le N\le 200$
• $1\le X_1<X_2<\dots<X_N\le 10^{9}$
• $1\le A_i\le 5000\ (1\le i\le N)$

Input

$N$
$X_1$ $X_2$ $\dots$ $X_N$
$A_1$ $A_2$ $\dots$ $A_N$

Output

If it is impossible to make all elements of $A$ equal to $0$, print $-1$. If it is possible, print the minimum distance traveled.

Sample

3
1 2 3
1 2 1

3

2
1 2
1 3

-1

10
2 3 5 7 11 13 17 19 23 29
5000 5000 5000 5000 5000 5000 5000 5000 5000 5000

130001