Description: The graph is called tree if it is connected and has no cycles. Suppose the tree is rooted at some vertex. Then tree is called to be perfect $$$k$$$-ary tree if each vertex is either a leaf (has no children) or has exactly $$$k$$$ children. Also, in perfect $$$k$$$-ary tree all leafs must have same depth. For example, the picture below illustrates perfect binary tree with $$$15$$$ vertices: There is a perfect $$$k$$$-ary tree with $$$n$$$ nodes. The nodes are labeled with distinct integers from $$$1$$$ to $$$n$$$, however you don't know how nodes are labelled. Still, you want to find the label of the root of the tree. You are allowed to make at most $$$60 \cdot n$$$ queries of the following type: - "? $$$a$$$ $$$b$$$ $$$c$$$", the query returns "Yes" if node with label $$$b$$$ lies on the path from $$$a$$$ to $$$c$$$ and "No" otherwise. Both $$$a$$$ and $$$c$$$ are considered to be lying on the path from $$$a$$$ to $$$c$$$. When you are ready to report the root of the tree, print - "! $$$s$$$", where $$$s$$$ is the label of the root of the tree. It is possible to report the root only once and this query is not counted towards limit of $$$60 \cdot n$$$ queries. Input Format: None Output Format: None Note: The tree in the example is as follows: The input and output for example illustrate possible interaction on that test (empty lines are inserted only for clarity). The hack corresponding to the example would look like: