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code_segments/segment_218.txt

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+This is an interactive problem.
+
+Misuki has chosen a secret tree with $n$ nodes, indexed from $1$ to $n$, and asked you to guess it by using queries of the following type:
+
+  * "? a b" — Misuki will tell you which node $x$ minimizes $|d(a,x) - d(b,x)|$, where $d(x,y)$ is the distance between nodes $x$ and $y$. If more than one such node exists, Misuki will tell you the one which minimizes $d(a,x)$. 
+
+Find out the structure of Misuki's secret tree using at most $15n$ queries!
+
+Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 200$) — the number of test cases.
+
+Each test case consists of a single line with an integer $n$ ($2 \le n \le 1000$), the number of nodes in the tree.
+
+It is guaranteed that the sum of $n$ across all test cases does not exceed $1000$.
+
+
+
+A tree is an undirected acyclic connected graph. A tree with $n$ nodes will always have $n-1$ edges.
+
+In the example case, the answer to "? 1 2" is $1$. This means that there is an edge between nodes $1$ and $2$.
+
+The answer to "? 1 3" is $1$. This means that there is an edge between nodes $1$ and $3$.
+
+The answer to "? 1 4" is $3$. It can be proven that this can only happen if node $3$ is connected to both node $1$ and $4$.
+
+The edges of the tree are hence $(1,2)$, $(1,3)$ and $(3,4)$.