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Ada is one of the best hairdressers in ChefLand. She invented a very cool hair style and named it "power tree".

A power tree with degree $l$ — let's denote it by $PT(l)$ — is a directed graph, which can be constructed recursively as follows:
$PT(0)$ consists of a single node.
For $l > 0$:
- Create one node $u$ — the root of power tree $PT(l)$.
- Construct all power trees with smaller degrees, i.e. $PT(0), PT(1), \dots, PT(l-1)$.
- For each of the tree created in the previous step, add a directed edge from $u$ to its root.

Today, Ada is going to cut the hair of some customers. Of course, all of them want to have a power tree hair style!

A customer's uncut hair is represented by a directed graph with $N$ vertices (numbered $1$ through $N$) and exactly one edge between each pair of vertices. Ada should remove some edges (possibly none) from this graph in such a way that the resulting graph is a power tree. Note that she is not allowed to remove vertices!

Can you help Ada find the edges she should remove?

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
Each of the next $N \choose 2$ lines contains two space-separated integers $u$ and $v$ describing a directed edge from vertex $u$ to vertex $v$. The edges are numbered $1$ through $N \choose 2$ in this order.

------ Output ------
For each test case:
If it is impossible to create a power tree, print a single line containing one integer $-1$.
Otherwise, print two lines. The first of these lines should contain a single integer $e$ denoting the number of edges to remove. The second line should contain $e$ space-separated integers denoting the numbers of the edges to remove.

If there are multiple answers, you may print any one.

------ Constraints ------
$1 ≤ T ≤ 128$
$2 ≤ N ≤ 256$
$1 ≤ u, v ≤ N$
there is exactly one edge between each pair of vertices

----- Sample Input 1 ------
1

4

1 4

2 1

2 4

3 1

3 2

3 4
----- Sample Output 1 ------
3

1 3 4
----- explanation 1 ------
Example case 1: Ada should remove edges $(1, 4)$, $(2, 4)$ and $(3, 1)$. The resulting graph is a power tree with degree $l=2$.

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