Score : $1400$ points

Problem Statement

You are given $P$, a permutation of $(1,\ 2,\ ...\ N)$.

A string $S$ of length $N$ consisting of 0 and 1 is a good string when it meets the following criterion:

• The sequences $X$ and $Y$ are constructed as follows:- First, let $X$ and $Y$ be empty sequences.
  • For each $i=1,\ 2,\ ...\ N$, in this order, append $P_i$ to the end of $X$ if $S_i=$ 0, and append it to the end of $Y$ if $S_i=$ 1.
• First, let $X$ and $Y$ be empty sequences.
• For each $i=1,\ 2,\ ...\ N$, in this order, append $P_i$ to the end of $X$ if $S_i=$ 0, and append it to the end of $Y$ if $S_i=$ 1.
• If $X$ and $Y$ have the same number of high elements, $S$ is a good string. Here, the $i$-th element of a sequence is called high when that element is the largest among the elements from the $1$-st to $i$-th element in the sequence.

Determine if there exists a good string. If it exists, find the lexicographically smallest such string.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq P_i \leq N$
• $P_1,\ P_2,\ ...\ P_N$ are all distinct.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$P_1$ $P_2$ $...$ $P_N$

Output

If a good string does not exist, print -1. If it exists, print the lexicographically smallest such string.

6
3 1 4 6 2 5

001001

Let $S=$ 001001. Then, $X=(3,\ 1,\ 6,\ 2)$ and $Y=(4,\ 5)$. The high elements in $X$ is the first and third elements, and the high elements in $Y$ is the first and second elements. As they have the same number of high elements, 001001 is a good string. There is no good string that is lexicographically smaller than this, so the answer is 001001.

5
1 2 3 4 5

-1

7
1 3 2 5 6 4 7

0001101

30
1 2 6 3 5 7 9 8 11 12 10 13 16 23 15 18 14 24 22 26 19 21 28 17 4 27 29 25 20 30

000000000001100101010010011101