Liu Like has placed N bomb(s) on the ground. If one bomb blasted, it will destroy all the enemy in the circle of which the center is the position of the bomb and the radius is 1. Now, please calculate the total covering area for power of the N bomb(s).

Input

The fisrt line contains one integer N(0 < N <= 100). Then, there are N line(s) following, each of the line contain two integer X, Y(-100 <= X, Y <= 100) which stand for the coordinate of one bomb.

Output

There is only one line, which contain the total area. Accurate to two digit after decimal point.

Sample Input
3
1 1
1 2
2 2
Sample Output
6.84