The Maximum Subtree

Assume that you have k one-dimensional segments s_1, s_2, ... s_k (each segment is denoted by two integers — its endpoints). Then you can build the following graph on these segments. The graph consists of k vertexes, and there is an edge between the i-th and the j-th vertexes (i ≠ j) if and only if the segments s_i and s_j intersect (there exists at least one point that belongs to both of them).

For example, if s_1 = [1, 6], s_2 = [8, 20], s_3 = [4, 10], s_4 = [2, 13], s_5 = [17, 18], then the resulting graph is the following:

A tree of size m is good if it is possible to choose m one-dimensional segments so that the graph built on these segments coincides with this tree.

You are given a tree, you have to find its good subtree with maximum possible size. Recall that a subtree is a connected subgraph of a tree.

Note that you have to answer q independent queries.

Input

The first line contains one integer q (1 ≤ q ≤ 15 ⋅ 10^4) — the number of the queries.

The first line of each query contains one integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of vertices in the tree.

Each of the next n - 1 lines contains two integers x and y (1 ≤ x, y ≤ n) denoting an edge between vertices x and y. It is guaranteed that the given graph is a tree.

It is guaranteed that the sum of all n does not exceed 3 ⋅ 10^5.

Output

For each query print one integer — the maximum size of a good subtree of the given tree.

Example

Input

1 10 1 2 1 3 1 4 2 5 2 6 3 7 3 8 4 9 4 10

Output

8

Note

In the first query there is a good subtree of size 8. The vertices belonging to this subtree are {9, 4, 10, 2, 5, 1, 6, 3}.

inputFormat

Input

The first line contains one integer q (1 ≤ q ≤ 15 ⋅ 10^4) — the number of the queries.

The first line of each query contains one integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of vertices in the tree.

Each of the next n - 1 lines contains two integers x and y (1 ≤ x, y ≤ n) denoting an edge between vertices x and y. It is guaranteed that the given graph is a tree.

It is guaranteed that the sum of all n does not exceed 3 ⋅ 10^5.

outputFormat

Output

For each query print one integer — the maximum size of a good subtree of the given tree.

Example

Input

1 10 1 2 1 3 1 4 2 5 2 6 3 7 3 8 4 9 4 10

Output

8

Note

In the first query there is a good subtree of size 8. The vertices belonging to this subtree are {9, 4, 10, 2, 5, 1, 6, 3}.

样例

1
10
1 2
1 3
1 4
2 5
2 6
3 7
3 8
4 9
4 10

8

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