Nested Ranges Check

Given $nn$ ranges, your task is to determine for each range if it contains some other range and if some other range contains it.

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

Input

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

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

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).