Two Stacks Sorting

• Time limit: 1.00 s
• Memory limit: 512 MB

You are given an input list that consists of $n$ numbers. Each integer between $1$ and $n$ appears exactly once in the list.

Your task is to create a sorted output list using two stacks. On each move you can do one of the following:

• Move the first number from the input list to a stack
  
• Move a number from a stack to the end of the output list
  

Input

The first input line has an integer $n$.

The second line has $n$ integers: the contents of the input list.

Output

Print $n$ integers: for each number the stack where it is moved ($1$ or $2$).

You can print any valid solution. If there are no solutions, print "IMPOSSIBLE".

Constraints

• $1 \le n \le 2 \cdot 10^5$
  

Example

Input:
5
2 3 1 5 4

Output:
1 2 1 1 2