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Cats And Tree

<a href="https://www.codechef.com/problems/CATS">https://www.codechef.com/problems/CATS</a>

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Cats And Tree

hard

https://www.codechef.com/problems/CATS

Constraints

.

Format

Input

.

Output

.

Example

Sample Input

10 0 1 2 3 3 1 6 6 6 1 5 6 3 4 2 1 7 8 9 10

Sample Output

4 1 2 2 0 0 1 1 1 1

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