We consider a sequence S₁ is equal to a sequence S₂, if and only if they satisfy the following conditions:

• The length of them are equal.
• Let Len be the length of them. For each i, j (1 <= i, j <= Len, i != j):If S₁[i] is smaller than S₁[j], S₂[i] must be smaller than S₂[j]; If S₁[i] is greater than S₁[j], S₂[i] must greater than S₂[j].

Now you are given a sequence S and another N sequences T₁, T₂ …. T_N.

We say position i is OK, if and only if S [1..i] contains a suffix which is equal to a sequence from { T₁, T₂ ... T_N }. You need to print the positions which is OK in increasing order.

Input

Multiple test cases, the number of them(no more than 3) is given in the very first line.

For each test case:

• The first line contains an integer M (M > 1) which denote the number of sequences. i.e. M = N + 1.
• M * 2 lines follow, each two lines describe one sequence. For each two lines, the first line contains an integer L which denote the length of this sequence. The second line contains L integers (all the integers don't exceed 2³¹-1) that represent this sequence. The first sequence described is S, the next N sequences represent T₁ ... T_N.
• You can assume that there are no same integer in any one sequence.
• The length of S is no more than 400000, and the total length of T is no more than 100000.

Output

For each test case: Print the positions which is OK in increasing order.

Example

Input:
2
2
1
1
1
2
3
3
3 1 2
2
4 5
2
10 1

Output:
1
2
3