Gas Station

Problem statement

An electric shuttle visits charging stops on a circular route. At stop i it receives gas[i] energy and spends cost[i] to reach the next stop. It starts empty and has unlimited capacity. Find the starting index for one complete lap without negative energy. If a valid start exists, it is unique.

Input format

First line: n. Second line: n energy gains. Third line: n travel costs.

Output format

Print the zero-based starting index, or -1 if no complete lap is possible.

Constraints

1 <= n <= 100000; 0 <= gains and costs <= 10000; at most one valid start.

Sample input

3
0 5 0
2 1 2

Sample output

1