There are $N$ villages numbered $1$ to $N$. The villages are connected through bi-directional paths in between them. The whole network is in the form of a tree.
Each village has only $1$ fighter but they help each other in times of crisis by sending their fighter to the village in danger through paths along the villages. Defeating a fighter will mean conquering his village. In particular, If village $X$ is under attack, all villages having a path to $X$ will send their fighters for help.
Naruto wants to conquer all the villages. But he cannot take on so many fighters at the same time so he plans to use a secret technique with which he can destroy any $1$ village (along with paths connected to it) in the blink of an eye. However, it can be used only once. He realized that if he destroys any village, say $X$, the maximum number of fighters he has to fight at once reduces to $W$. He wants $W$ to be as small as possible. Help him find the optimal $X$.
In case of multiple answers, choose the smallest value of $X$.

-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- First Line contains $N$.
- Next $N - 1$ lines contain $U, V$, denoting a path between village $U$ and $V$.

-----Output:-----
- For each Test case, print in a new line, optimal $X$ and corresponding value of $W$.

-----Constraints-----
- $1 \leq T \leq 10$
- $3 \leq N \leq 10^5$
- $1 \leq U, V \leq N$
- $U != V$

-----Sample Input:-----
2
5
1 2
1 3
2 4
3 5
3
1 2
2 3

-----Sample Output:-----
1 2
2 1

-----EXPLANATION:-----
Sample 1: By destroying village $1$, The fighters Naruto will be fighting at the same time will be from villages $[2, 4]$ and $[3, 5]$. For this $W$ = $2$. No other choice can give lesser $W$. Hence $1$ is optimal choice.

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