A charity gala hands out n prize envelopes to contestants, each holding a non-negative integer amount of prize money. The organizers want to know whether one contestant's prize completely dominates the field: specifically, whether the largest prize amount is at least twice as large as every other contestant's prize. It is guaranteed that the largest prize amount in the list is unique (no ties for the top prize). If the largest prize dominates in this way, report its 0-indexed position in the list; otherwise, report that no such dominant prize exists.

Input format

• Line 1: integer n, the number of contestants.
• Line 2: n space-separated integers, the prize amount for each contestant, given in order (0-indexed).

Output format

Print a single integer: the 0-indexed position of the largest prize if it is at least twice every other prize in the list, otherwise print -1.

Constraints

• 1 <= n <= 50
• 0 <= prize_i <= 100
• The largest value among the prizes is unique.

4
3 6 1 0

1

4
1 2 3 4

-1