Phineas and Ferb are playing an interesting game. They have N piles of stones numbered from 1 to N in front of them. The \(i^{th}\) pile contains \(A_{i}\) stones. Both of them play turn wise and optimally with Phineas starting first.

In each turn, a player can remove any number of stones from any of the pile which has positive amount of stones left in it. A player loses when he cannot remove any stone and all piles are already empty.

You are given Q queries. Each query contains two integers integer l and r. For each query, your task is to tell winner of the game if it was only played on the piles from range l to r (both inclusive).

Note that, each query is independent from other queries and does not affect them in any way.

Input:
The first line of the input contains a single integer N denoting the number of piles.
The second line contains N space-separated integers where \(i^{th}\) integer denotes the amount of stones in \(i^{th}\) pile.
The third line contains an integer Q denoting the number of queries.
Next Q lines contains two single space separated integers l and r as described in the problem statement.

Output:
Print winner of each query in a separate line. Output "Phineas" if Phineas wins or "Ferb" if Ferb wins.

Constraints:

• \(1 ≤ N ≤ 5 * 10^{5}\)
• \(1 ≤ A_{i} ≤ 10^{9}\)
• \(1 ≤ Q ≤ 2 * 10^{5}\)
• \(1 ≤ l \le r ≤ N\)