You are given $N$ light sources on the plane, each of which illuminates the angle of $2\pi/N$ with the vertex in the source point (including its sides).</p>

You must choose the direction of the illuminated angle for each of these sources, so that the whole plane is illuminated. It can be proved that this is always possible.

A light source itself casts no shadow and does not interfere with light beams from the other sources.

입력 형식

The first line of the input file contains $N$ --- the number of light sources ($3 \le N \le 30$). Next $N$ lines contain two integer numbers each --- the coordinates of the light sources. All coordinates do not exceed $100$ by their absolute value. No two sources coincide.

출력 형식

Print $N$ real numbers --- for each light source specify an angle that the bisector of the illuminated angle makes with $OX$ axis, counterclockwise. Print at least six digits after the decimal point. No angle must exceed $100 \pi$ by its absolute value.</p>

예제 입력

3
0 0
2 0
1 1

예제 출력

0.52359877559829887
2.61799387799149437
4.71238898038468986

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