Problem Description
Let S be a number string, and occ(S,x) means the times that number x occurs in S.
i.e. S=(1,2,2,1,3),occ(S,1)=2,occ(S,2)=2,occ(S,3)=1.
String u,w are matched if for each number i, occ(u,i)=occ(w,i) always holds.
i.e. (1,2,2,1,3)≈(1,3,2,1,2).
Let S be a string. An integer k is a full Abelian period of S if S can be partitioned into several continous substrings of length k, and all of these substrings are matched with each other.
Now given a string S, please find all of the numbers k that k is a full Abelian period of S.
Input
The first line of the input contains an integer T(1≤T≤10), denoting the number of test cases.
In each test case, the first line of the input contains an integer n(n≤100000), denoting the length of the string.
The second line of the input contains n integers S1,S2,S3,...,Sn(1≤Si≤n), denoting the elements of the string.
Output
For each test case, print a line with several integers, denoting all of the number k. You should print them in increasing order.
Sample Input
2
6
5 4 4 4 5 4
8
6 5 6 5 6 5 5 6
Sample Output
3 6
2 4 8
