Nested Ranges Check

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