13868번 - Counting Self-Rotating Subsets 다국어

문제

A set of points in the plane is self-rotating if there is a point P, the center, and an angle α, expressed in degrees, where 0 < α < 360, such that the rotation of the plane, with center P and angle α, maps every point in the set to some point also in the set.

You are given a set of N distinct points, all having integer coordinates. Find the number of distinct subsets of size 1, 2, . . . , N that are self-rotating. Two subsets are considered distinct if one contains a point that the other does not contain.

입력

The first line of the input contains one integer N representing the number of points in the input set (1 ≤ N ≤ 1000). Each of the following N lines describes a different point of the set, and contains two integers X and Y giving its coordinates in a Cartesian coordinate system (−10⁹ ≤ X, Y ≤ 10⁹ ). All points in the input set are distinct.

출력

Output a single line containing N integers S₁, S₂, . . . , S_N . For i = 1, 2, . . . , N the integer S_i must be the number of subsets of i points of the input set that are self-rotating. Since these numbers can be very big, output them modulo 10⁹ + 7.

제한

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