There are $N$ toys numbered from $1$ to $N$, and $N-1$ boxes numbered from $1$ to $N-1$. Toy $i\ (1 \leq i \leq N)$ has a size of $A_i$, and box $i\ (1 \leq i \leq N-1)$ has a size of $B_i$.

Takahashi wants to store all the toys in separate boxes, and he has decided to perform the following steps in order:

1. Choose an arbitrary positive integer $x$ and purchase one box of size $x$.
2. Place each of the $N$ toys into one of the $N$ boxes (the $N-1$ existing boxes plus the newly purchased box). Here, each toy can only be placed in a box whose size is not less than the toy's size, and no box can contain two or more toys.

He wants to execute step $2$ by purchasing a sufficiently large box in step $1$, but larger boxes are more expensive, so he wants to purchase the smallest possible box.

Determine whether there exists a value of $x$ such that he can execute step $2$, and if it exists, find the minimum such $x$.

The input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\dots$ $A_N$

$B_1$ $B_2$ $\dots$ $B_{N-1}$

If there exists a value of $x$ such that Takahashi can execute step $2$, print the minimum such $x$. Otherwise, print -1.

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq 10^9$
• All input values are integers.

Consider the case where $x=3$ (that is, he purchases a box of size $3$ in step $1$).

If the newly purchased box is called box $4$, toys $1,\dots,4$ have sizes of $5$, $2$, $3$, and $7$, respectively, and boxes $1,\dots,4$ have sizes of $6$, $2$, $8$, and $3$, respectively. Thus, toy $1$ can be placed in box $1$, toy $2$ in box $2$, toy $3$ in box $4$, and toy $4$ in box $3$.

On the other hand, if $x \leq 2$, it is impossible to place all $N$ toys into separate boxes. Therefore, the answer is $3$.

No matter what size of box is purchased in step $1$, no toy can be placed in box $2$, so it is impossible to execute step $2$.