5392：Infoplane in Tina Town

There is a big stone with smooth surface in Tina Town. When people go towards it, the stone surface will be lighted and show its usage. This stone was a legacy and also the center of Tina Town’s calculation and control system. also, it can display events in Tina Town and contents that pedestrians are interested in, and it can be used as public computer. It makes people’s life more convenient (especially for who forget to take a device).

Tina and Town were playing a game on this stone. First, a permutation of numbers from $1$ to $n$ were displayed on the stone. Town exchanged some numbers randomly and Town recorded this process by macros. Town asked Tine,”Do you know how many times it need to turn these numbers into the original permutation by executing this macro? Tina didn’t know the answer so she asked you to find out the answer for her.

Since the answer may be very large, you only need to output the answer modulo $3*{2}^{30}+1=3221225473$ (a prime).

The first line is an integer $T$ representing the number of test cases. $ T \leq 5$

For each test case, the first line is an integer $n$ representing the length of permutation. $ n \leq 3*{10}^{6} $

The second line contains $n$ integers representing a permutation $A_1...A_n$. It is guaranteed that numbers are different each other and all $A_i$ satisfies ( $1 \leq A_i \leq n$ ).

For each test case, print a number $ans$ representing the answer.