実行時間制限: 2 sec / メモリ制限: 256 MB

### Problem

There's a Japanese dish called 'Yakiniku', which is very similar to barbecue. You roast some pieces of meat on a grill to cook 'Yakiniku'.

You have a grill that can roast any number of pieces of meat on it at once.
You want to make `N` pieces of 'Yakiniku' using that grill.

'Yakiniku' is a very tender dish that the `i`-th piece of meat must be put on the grill at the time `s_i`, and must be picked up at the time `t_i` sharp. If you pick the piece of meat later than `t_i` that piece is 'scorched'. If you pick the piece of meat earlier than `t_i` that piece is 'underdone'.

However, when you pick the `i`-th piece of meat at the time `t_i`, you totally forget where you put the `i`-th piece of meat on, so you pick `1` piece of meat from the grill at random.
Calculate the probability of each piece of meat picked up 'underdone' and 'scorched'.

### Input

Input is given in the following format.

Ns_1t_1s_2t_2:s_Nt_N

- On the first line, you will be given the integer
`N (1 \leq N \leq 100,000)`, the number of pieces of meat you are going to cook 'Yakiniku'. - Following
`N`lines consists of two integers`s_i,t_i (0 \leq s_i < t_i \leq 10^9)`, the time you put the`i`-th meat on the grill and the time you have to pick up that meat from the grill.`s_1,s_2,...,s_N,t_1,t_2,...,t_N`are distinct from each other.

### Output

Output `N` lines. The `i`-th `(1 \leq i \leq N)` line should contain the probability of `i`-th piece of meat picked up from the grill 'underdone' and 'scorched' separated by space.
Your answer is considered correct if it has an absolute or relative error less than `10^{-7}`.

### Input Example 1

2 1 3 2 4

### Output Example 1

0.0 0.5 0.5 0.0

Think of the `1`st piece of meat. At the time `3` there are `2` pieces of meat on the grill. You pick the `2`nd piece of meat with probability `1/2` and in that case at the time `4` the `1`st meat will be picked up 'scorched'.

Think of the `2`nd piece of meat. At the time `3` the `2`nd piece of meat is taken from the grill with probability `1/2` and is 'underdone'.

### Input Example 2

5 1 2 3 4 5 10 6 9 7 8

### Output Example 2

0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.6666666667 0.0000000000 0.3333333333 0.3333333333 0.0000000000 0.6666666667

### Input Example 3

1 0 1000000000

### Output Example 3

0 0