CSES - Two Stacks Sorting
  • Time limit: 1.00 s
  • Memory limit: 512 MB

You are given an input list that consists of nn numbers. Each integer between 11 and nn 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 nn.

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

Output

Print nn integers: for each number the stack where it is moved (11 or 22).

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

Constraints

  • 1n21051 \le n \le 2 \cdot 10^5

Example

Input:

5
2 3 1 5 4

Output:

1 2 1 1 2