Background

Special for beginners, ^_^

Description

We can classify strings made up of 0 and 1 into three types: an all-0 string is called a $B$ string, an all-1 string is called an $I$ string, and a string containing both 0 and 1 is called an $F$ string.

An $FBI$ tree is a kind of binary tree whose node types are also of three kinds: $F$ nodes, $B$ nodes and $I$ nodes. Given a 01 string $S$ of length $2^N$, we can construct an $FBI$ tree $T$ by the following recursive construction:

The root of $T$ is $R$, and its type is the same as the type of the string $S$;

If the length of $S$ is greater than $1$, split $S$ from the middle into a left substring $S1$ and a right substring $S2$ of equal length; construct the left subtree $T1$ of $R$ from the left substring $S1$, and the right subtree $T2$ of $R$ from the right substring $S2$.

Now given a 01 string of length $2^N$, construct an $FBI$ tree using the construction above, and output its postorder traversal sequence.

Format

Input

The first line of the input is an integer $N\ (0 \le N \le 10)$, and the second line is a 01 string of length $2^N$.

Output

Output one line containing exactly one string: the postorder traversal sequence of the $FBI$ tree.

Samples

3
10001011

IBFBBBFIBFIIIFF

Limitation

1s, 1024KiB for each test case.

For $40\%$ of the data, $N \le 2$;

For $100\%$ of the data, $N \le 10$.