Problems

# Attack of aliens

Time limit 1 second
Memory limit 128 MiB

The city of Ensk is attacked by a fleet of aliens. The fleet consists of n spaceships, each of which has the shape of an isosceles right triangle.

The nose of an alien ship is considered to be a vertex with right angle, and the axis of the ship is the height that is lowered to the hypotenuse.

The aliens flew from the northeast, and froze in such a position that all the axes of the ships are directed strictly to the south-west.

The only way to make the damage to an alien army is to start a laser beam from some point on the Earth's surface vertically upwards. When launched, the ray burns through all the enemy ships through which it passes (even those that it touches along the border). But this shot will hurt the aliens only if all n ships are hit at the same time.

The military authorities of the Ensk city decided to strike at the enemy troops. For this, it was decided to place the lasers in one of the points above which all n enemy ships are located.

Help the military to determine the area of the territory where you can put the laser.

## Input data

The first line contains one integer n (1n100) - the number of alien ships.

Each of the next n lines contains the position of the next ship. The description consists of three integers x[i], y[i] and s[i], where x[i] and y[i] are nose coordinates, s[i] is the size of the ship. Since the ship has the shape of an isosceles rectangular triangle, the military decided to call the size of the ship the length of cathetus.

The ship's sizes are positive numbers not exceeding 1000. The coordinates of ship's noses do not exceed 10^5 in absolute value.

## Output data

Print the area of the territory, above which located all the alien ships. Print the answer with three decimal digits.

## Examples

Input example #1
3
2 4 6
4 2 7
3 3 5

Output example #1
4.500

Source 2006, XIV St. Petersburg School Programming Team Championship, November 6, Problem А