Two Stacks Sorting

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