Baltic Olympiad in Informatics: 2002 Day 1, Problem 3

There are given ~n~ isosceles right triangles on a plane. Each triangle can be described by three integers ~x, y, m~. Vertices of such a triangle are points which have coordinates ~(x, y)~, ~(x+m, y)~ and ~(x, y+m)~.

Write a program which calculates the total area covered by triangles.

Constraints

~1 \le n \le 2\,000~

~|x_i|, |y_i| \le 10^7~

~1 \le m_i \le 1\,000~

Input Specification

The first line of input contains one positive integer ~n~, the number of triangles on a plane.

The next ~n~ lines describe the triangles, one triangle per line. Each line contains three space-separated integers ~x_i~, ~y_i~ and ~m_i~ ~(1 \le i \le n)~.

Output Specification

Output one number with exactly one digit after the decimal point - the total area covered by triangles.

Sample Input

5
-5 -3 6
-1 -2 3
0 0 2
-2 2 1
-4 -1 2

Sample Output

24.5