Ciel and a new island

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Chef Ciel develops a new island with her restaurants. In the island, Ciel intends to built N restaurants, and the coordinate of the i-th restaurant will be (xi, yi). In addition, Ciel is going to create K roads, whose location is not decided yet. Each road must be a infinitely long straight line. Let di be the distance between the i-th restaurant and the nearest road from the i-th restaurant. Cie

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