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

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