Copil Copac is given a list of $$$n-1$$$ edges describing a tree of $$$n$$$ vertices. He decides to draw it using the following algorithm:

Step $$$0$$$: Draws the first vertex (vertex $$$1$$$). Go to step $$$1$$$.
Step $$$1$$$: For every edge in the input, in order: if the edge connects an already drawn vertex $$$u$$$ to an undrawn vertex $$$v$$$, he will draw the undrawn vertex $$$v$$$ and the edge. After checking every edge, go to step $$$2$$$.
Step $$$2$$$: If all the vertices are drawn, terminate the algorithm. Else, go to step $$$1$$$.

The number of readings is defined as the number of times Copil Copac performs step $$$1$$$.

Find the number of readings needed by Copil Copac to draw the tree.

Input

Each test contains multiple test cases. The first line of input contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$) — the number of vertices of the tree.

The following $$$n - 1$$$ lines of each test case contain two integers $$$u_i$$$ and $$$v_i$$$ ($$$1 \le u_i, v_i \le n$$$, $$$u_i \neq v_i$$$) — indicating that $$$(u_i,v_i)$$$ is the $$$i$$$-th edge in the list. It is guaranteed that the given edges form a tree.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output the number of readings Copil Copac needs to draw the tree.

Note

In the first test case:

After the first reading, the tree will look like this:

$\text{[math]}$

After the second reading:

$\text{[math]}$

Therefore, Copil Copac needs $$$2$$$ readings to draw the tree.

Copil Copac Draws Trees

Examples