High Elements

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.
• 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.

Examples

Input

6 3 1 4 6 2 5

Output

001001

Input

5 1 2 3 4 5

Output

-1

Input

7 1 3 2 5 6 4 7

Output

0001101

Input

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

Output

000000000001100101010010011101

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N P_1 P_2 ... P_N

outputFormat

Output

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

Examples

Input

6 3 1 4 6 2 5

Output

001001

Input

5 1 2 3 4 5

Output

-1

Input

7 1 3 2 5 6 4 7

Output

0001101

Input

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

Output

000000000001100101010010011101

样例

6
3 1 4 6 2 5

001001