Description

You are given a sequence of $2^N$ positive integers. In each round, these numbers are compared in the given order: the larger number stays, and the smaller number is eliminated, until only one number remains.

Now you are given the initial order of these $2^N$ numbers. Please find, for each number, the maximum round it can survive to.

Input Format

The first line contains an integer $N$.

The second line contains $2^N$ integers $A_i$, representing the numbers in the sequence.

Output Format

Output one line with $2^N$ integers, where the $i$-th integer represents the round that the $i$-th number can survive to.

2
1 4 3 2

2 0 1 1

4
5 3 2 6 4 8 7 1 2 4 3 3 6 4 8 1

1 2 2 1 1 0 1 3 2 1 2 2 1 1 0 3

1
1 1

0 0

Hint

[Sample Explanation #2]

[Constraints]

For $100\%$ of the testdata, $1\le N\le 20$, $0\le A_i\le 1\times 10^9$.

[Note]

The scoring of this problem follows the original COCI settings, with a full score of $100$.

This problem is translated from COCI2016_2017 CONTEST #6 T3 TURNIR.

Translated by ChatGPT 5