You are given two arrays \(a_1, a_2, \dots, a_n\) and \(b_1, b_2, \dots, b_n\). In each step, you can set \(a_i = a_i - b_i\) if \(a_i \ge b_i\). Determine the minimum number of steps that are required to make all \(a\)'s equal.

Input format

• First line: \(n\) 
• Second line: \(a_1, a_2, \dots, a_n\)
• Third line: \(b_1, b_2, \dots, b_n\)

Output format

Print the minimum number of steps that are required to make all \(a\)'s equal. If it is not possible, then print -1.

Constraints

\(0 \le n, a_i, b_i \le 5000 \)

Sample input

25 64 3

Sample output

-1