CSES - Nested Ranges Check
• Time limit: 1.00 s
• Memory limit: 512 MB
Given $n$ ranges, your task is to determine for each range if it contains some other range and if some other range contains it.

Range $[a,b]$ contains range $[c,d]$ if $a \le c$ and $d \le b$.

Input

The first input line has an integer $n$: the number of ranges.

After this, there are $n$ lines that describe the ranges. Each line has two integers $x$ and $y$: the range is $[x,y]$.

You may assume that no range appears more than once in the input.

Output

First print a line that describes for each range (in the input order) if it contains some other range (1) or not (0).

Then print a line that describes for each range (in the input order) if some other range contains it (1) or not (0).

Constraints
• $1 \le n \le 2 \cdot 10^5$
• $1 \le x < y \le 10^9$
Example

Input:
4 1 6 2 4 4 8 3 6

Output:
1 0 0 0 0 1 0 1