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code_segments/segment_93.txt
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Two hungry red pandas, Oscar and Lura, have a tree $T$ with $n$ nodes. They are willing to perform the following shuffle procedure on the whole tree $T$ exactly once. With this shuffle procedure, they will create a new tree out of the nodes of the old tree.
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1. Choose any node $V$ from the original tree $T$. Create a new tree $T_2$, with $V$ as the root. 2. Remove $V$ from $T$, such that the original tree is split into one or more subtrees (or zero subtrees, if $V$ is the only node in $T$). 3. Shuffle each subtree with the same procedure (again choosing any node as the root), then connect all shuffled subtrees' roots back to $V$ to finish constructing $T_2$.
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After this, Oscar and Lura are left with a new tree $T_2$. They can only eat leaves and are very hungry, so please find the maximum number of leaves over all trees that can be created in exactly one shuffle.
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Note that leaves are all nodes with degree $1$. Thus, the root may be considered as a leaf if it has only one child.
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The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
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The first line of every test case contains a single integer $n$ ($2 \leq n \leq 2 \cdot 10^5$) — the number of nodes within the original tree $T$.
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The next $n - 1$ lines each contain two integers $u$ and $v$ ($1 \leq u, v \leq n$) — an edge within the original tree $T$. The given edges form a tree.
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The sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.
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For each test case, output a single integer — the maximum number of leaves achievable with exactly one shuffle procedure on the whole tree.
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In the first test case, it can be shown that the maximum number of leaves is $4$. To accomplish this, we can start our shuffle with selecting node $3$ as the new root.
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 Next, we are left only with one subtree, in which we can select node $2$ to be the new root of that subtree.  This will force all $3$ remaining nodes to be l
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