1830A · Copil Copac Draws Trees

Problem: 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 Format: 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 Format: 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:

After the second reading:

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