This is an interactive problem.

The judge has a hidden rooted full binary tree with *n* leaves. A full binary tree is one where every node has either 0 or 2 children. The nodes with 0 children are called the leaves of the tree. Since this is a full binary tree, there are exactly 2*n* - 1 nodes in the tree. The leaves of the judge's tree has labels from 1 to *n*. You would like to reconstruct a tree that is isomorphic to the judge's tree. To do this, you can ask some questions.

A question consists of printing the label of three distinct leaves *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">3</sub>. Let the depth of a node be the shortest distance from the node to the root of the tree. Let *LCA*(*a*, *b*) denote the node with maximum depth that is a common ancestor of the nodes *a* and *b*.

Consider *X* = *LCA*(*a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>), *Y* = *LCA*(*a*<sub class="lower-index">2</sub>, *a*<sub class="lower-index">3</sub>), *Z* = *LCA*(*a*<sub class="lower-index">3</sub>, *a*<sub class="lower-index">1</sub>). The judge will tell you which one of *X*, *Y*, *Z* has the maximum depth. Note, this pair is uniquely determined since the tree is a binary tree; there can't be any ties. 

More specifically, if *X* (or *Y*, *Z* respectively) maximizes the depth, the judge will respond with the string "X" (or "Y", "Z" respectively). 

You may only ask at most 10·*n* questions.
The first line of input will contain a single integer *n* (3 ≤ *n* ≤ 1 000) — the number of leaves in the tree.
For the first sample, the judge has the hidden tree:

<img class="tex-graphics" src="https://espresso.codeforces.com/2c9cae7de194cc1bc508ea7243ff4d0d509d34bd.png" style="max-width: 100.0%;max-height: 100.0%;"/>

Here is a more readable format of the interaction:
print("_RANDOM_GUESS_1690493126.23867")# 1690493126.2387068