There are given n isosceles right triangles on a plane. Each triangle can be described by three integers x,y,m (m>0). 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.

Input

The first line of the input contains one positive integer n (n <= 2000), the number of triangles on a plane.

The next n lines of the file describe the triangles, one triangle per line. Each line contains three integers x_i, y_i and m_i, separated by single spaces (1 <= i <= n, ‑10⁷ <= x_i <= 10⁷, ‑10⁷ <= y_i <= 10⁷, 0 < m_i <= 1000).

Output

On the first line of the output one number with exactly one digit after decimal point must be written – the total area covered by triangles.

Example

Input
5
-5 -3 6
-1 -2 3
 0 0 2
-2 2 1
-4 -1 2
Output
24.5