Question
Delivery Truck Fuel Circle

A delivery truck must travel around a circular route with N stations. At station i, the truck can collect fuel[i] units of fuel. Travelling from station i to the next station costs cost[i] units of fuel.

Return the index of a station from where the truck can complete the full circle, or -1 if it is impossible.

Input

The first line contains an integer KaTeX can only parse string typed expression.

The second line contains KaTeX can only parse string typed expression integers — KaTeX can only parse string typed expression.

The third line contains KaTeX can only parse string typed expression integers — KaTeX can only parse string typed expression.

Output

Print a single integer — a valid starting index, or KaTeX can only parse string typed expression.

Example
Example 1:
Input
5

1 2 3 4 5
3 4 5 1 2
Output
3


Example 2:
Input
3

2 3 4
3 4 3
Output
-1

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