B'"Flowing and passing like this, the water isn 't gone ultimately; Waxing and waning like that, the moon doesn 't shrink or grow eventually." "Everything is transient in a way and perennial in another." Kanno doesn 't seem to make much sense out of Mino 's isolated words, but maybe it 's time that they enjoy the gentle breeze and the night sky -- the inexhaustible gifts from nature. Gazing into the sky of stars, Kanno indulges in a night 's tranquil dreams. There is a set S of n points on a coordinate plane. Kanno starts from a point P that can be chosen on the plane. P is not added to S if it doesn 't belong to S . Then the following sequence of operations (altogether called a move) is repeated several times, in the given order: There are q queries each consisting of two integers (t_i, m_i) . For each query, you 're to help Kanno maximize the probability of the stopping position being the t_i -th element in S after m_i moves with a proper selection of P , and output this maximum probability. Note that according to rule 1, P should belong to at least one line that passes through at least two points from S . The first line contains a positive integer n ( 2 <= q n <= q 200 ) -- the number of points in S . The i -th of the following n lines contains two space-separated integers x_i and y_i ( -10^4 <= q x_i, y_i <= q 10^4 ) -- the coordinates of the i -th point in S . The input guarantees that for all 1 <= q i lt j <= q n , (x_i, y_i) neq (x_j, y_j) holds. The next line contains a positive integer q ( 1 <= q q <= q 200 ) -- the number of queries. Each of the following q lines contains two space-separated integers t and m ( 1 <= q t_i <= q n , 1 <= q m_i <= q 10^4 ) -- the index of the target point and the number of moves, respectively. Output q lines each containing a decima'...