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.

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 $T_2$.

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.

Note that leaves are all nodes with degree $1$. Thus, the root may be considered as a leaf if it has only one child.

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

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 $T$.

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.

The sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.

For each test case, output a single integer — the maximum number of leaves achievable with exactly one shuffle procedure on the whole tree.