Output Format

Print three space-separated positive integers on a single line: the index of the critical leaf node with the smallest index, the number of critical leaf nodes, and the bitwise XOR of the indices of all critical leaf nodes.

7 
1 
1 
2 
2 
3 
3

4 4 0 

Hint

[Sample explanation]

As shown, black nodes indicate Black-to-move nodes, and white nodes indicate White-to-move nodes.

All minimal Black-winning sets are $\{4, 5\}$ and $\{6, 7\}$.

All minimal White-winning sets are $\{4, 6\}$, $\{4, 7\}$, $\{5, 6\}$, and $\{5, 7\}$.

Therefore, the set of critical leaf nodes is $\{4, 5, 6, 7\}$.

• For $30\%$ of the testdata, $n \le 100$.
• For $40\%$ of the testdata, $n \le 1000$.
• For $50\%$ of the testdata, $n \le 10 ^ 4$, and the tree is randomly generated.
• For $100\%$ of the testdata, $1 \le n \le 2\times 10 ^ 5$, and for node $i$ ($i \ne 1$), the index of its parent is less than $i$.

Translated by ChatGPT 5