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