There are $N$ positive integers arranged in a circle. Now, the $i$\-th number is $A_i$. Takahashi wants the $i$\-th number to be $B_i$. For this objective, he will repeatedly perform the following operation: - Choose an integer $i$ such that $1 \leq i \leq N$. - Let $a, b, c$ be the $(i-1)$\-th, $i$\-th, and $(i+1)$\-th numbers, respectively. Replace the $i$\-th number with $a+b+c$. Here the $0$\-th number is the $N$\-th number, and the $(N+1)$\-th number is the $1$\-st number. Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.

Input is given from Standard Input in the following format: >$N$\ >$A_1$ $A_2$ $...$ $A_N$\ >$B_1$ $B_2$ $...$ $B_N$ #### Constraints - $3 \leq N \leq 2 \times 10^5$ - $1 \leq A_i, B_i \leq 10^9$ - All values in input are integers.

Print the minimum number of operations required, or `-1` if the objective cannot be achieved.

***For Sample #1:*** Takahashi can achieve his objective by, for example, performing the following operations: - Replace the second number with $3$. - Replace the second number with $5$. - Replace the third number with $7$. - Replace the first number with $13$.