Nested Ranges Count

• Time limit: 1.00 s
• Memory limit: 512 MB

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.

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.

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:
2 0 0 0
0 1 0 1