"Slipped, tumbled, Mountain is quiet and alone." is a haiku by Santōka Taneda (1882-1940).

Peng is a young climber who enjoys mountaineering really much. One day he was climbing a tall mountain alone when he, unfortunately, slipped. He started tumbling, rolling down the mountain.

The mountain (up to the point where Peng is at) is a monotone slope described by points such that and . The slope contains the following segments: , , and for all . For simplicity we consider Peng to be a segment of length , and we call the end of the segment Peng's "head".

We now describe the rolling process. Peng always rotates counter-clockwise (downhill) around his lowest contact point with the hill. Whenever he has a new (lower) contact point with the hill, he starts rolling from that point. He only stops rolling when his"head" has -coordinate .

Peng would like to know the total length his "head" travels in the rolling process. 

输入描述:

The first line contains an integer  ().
For each of the following  lines, the -th line contains two real numbers  and  with at most  digits of precision.

输出描述:

Output one real number, the total distance.
Your answer will be considered correct if its absolute or relative error does not exceed . Formally let your answer be  and jury's answer be . Your answer will be considered correct if .

1
0.5 0.5

2.094395102393195

2
0.2 0.8
1 1

4.465554239614399

备注:

It is guaranteed that during the rotation, when an end point of the segment is in contact with the hill, the point is not within  distance of points .