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

Example Output

2 0 0 0
0 1 0 1