문제

Farmer John and his archnemesis Farmer Nhoj are playing a game in a circular barn. There are $N$ ($1 \leq N \leq 10^5$) rooms in the barn, and the $i$th room initially contains $a_i$ cows ($1 \leq a_i \leq 5\cdot 10^6$). The game is played as follows:

Both farmers will always be in the same room. After entering a room, each farmer takes exactly one turn, with Farmer John going first. Both farmers initially enter room $1$.If there are zero cows in the current room, then the farmer to go loses. Otherwise, the farmer to go chooses an integer $P$, where $P$ must either be $1$ or a prime number at most the number of cows in the current room, and removes $P$ cows from the current room.After both farmers have taken turns, both farmers move to the next room in the circular barn. That is, if the farmers are in room $i$, then they move to room $i+1$, unless they are in room $N$, in which case they move to room $1$.

Determine the farmer that wins the game if both farmers play optimally.

입력

The input contains $T$ test cases. The first line contains $T$ ($1 \leq T \leq 1000$). Each of the $T$ test cases follow.

Each test case starts with a line containing $N$, followed by a line containing $a_1,\dots,a_N$.

It is guaranteed that the sum of all $N$ is at most $2\cdot 10^5$.

출력

For each test case, output the farmer that wins the game, either "Farmer John" or "Farmer Nhoj."

예제 입력 1

5
1
4
1
9
2
2 3
2
7 10
3
4 9 4

예제 출력 1

Farmer Nhoj
Farmer John
Farmer John
Farmer John
Farmer Nhoj

점수

Inputs 2-4 satisfy $N=1$.Inputs 1, 2, and 5-7 satisfy $a_i\le 1000$.Inputs 8-20 satisfy no additional constraints.