In laboratories of a certain company a new material called politoksyparen is tested. During the researches an interesting property has been discovered. A simple rod made of this material after being heated lengthens and bends so that it changes into an circular arc based on a chord, which is the shape of the rod at the beginning (this property concerns only rods of short diameters). Let’s assume that n rods with very short diameters and lengths l_i (1 <= l_i <= 100000) were used to verify this property, and while being heated they lengthened respectively by d_i (1 <= d_i <= 100), where d_i <= l_i / 2. As a unit we take one millimeter.

Task

Write a program that:

• reads from the text file PRE.IN a number of rods n, their lengths l_i and increases in lengths d_i,
• computes for each rod a distance between the middle of the chord and the middle of the arc after heating (assuming that politoksyparen has indeed the observed property, and rods really band into circular arcs while being heated); the result should be an integer which differs no more then 0,5 from the exact result,
• writes the solution in the text file PRE.OUT.

Input

Output

Example

the correct answer is the output file PRE.OUT:
87
237

Your program should look for the file PRE.IN in the current directory and produce the output file PRE.OUT in the current directory too. The file containing the source code of your program should have a name PRE.???, whereas you should put three-letter abbreviation of the used programming language name instead of ???. The same program in executable form should be written in the file PRE.EXE