## UNTITLED - Untitled Problem

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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 …. TN.

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 ... TN }. 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 ... TN.
• 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
```