S. Nested Ranges Count
time limit per test
2 s
memory limit per test
256 megabytes
input
standard input
output
standard output

Given $$$n$$$ ranges, your task is to count for each range how many other ranges it contains and how many other ranges contain 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.

Constraints:

  • $$$1 \le n \le 2\cdot 10^5$$$
  • $$$1 \le x \lt y \le 10^9$$$
Output

First print a line that describes for each range (in the input order) how many other ranges it contains.

Then print a line that describes for each range (in the input order) how many other ranges contain it.

Example
Input
4
1 6
2 4
4 8
3 6
Output
2 0 0 0 
0 1 0 1