Points

Time Limit: 10 Seconds    Memory Limit: 131072 KB

Peter and Bob are playing  a "Points"  game  on a math sheet of paper. Peter  places a few points on the paper  -  grid nodes. Bob wants to surround them  with  a  polygon so that all marked nodes are lying strictly within (not at the border)  the polygon. All sides of the polygon are along the sides or the diagonals of the  grid cells  and its  perimeter is  as  small  as possible.  You must  determine what is the perimeter of the polygon.

Input

The first line of the input file contains integer  N  –  the  number of points placed  by Peter  (1 ≤ N ≤ 100 000). Each of following N lines contains two integers x_i, y_i – the point coordinates placed by Peter. The coordinates by absolute value do not exceed 10⁶. Some points can match.

Output

You  need  to  print  one  number  –  the  perimeter of  the  required  polygon.  The answer should be printed with accuracy not less than 0.001.

Sample Input

1
0 0


2
1 1
1 2

Sample Output

5.656



7.656854

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