CSES - 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