Who visits early in the morning
In the Wonderful Forest, there are N unique characters, each residing in their own little house. Following the wise advice of the renowned forest character, Winnie-the-Pooh, every resident believes it's essential to rise early, freshen up, get dressed, and pay a visit to someone. Naturally, to act not just wisely, but very wisely, and to minimize travel time, each character will visit their nearest neighbor—the resident whose house is closest to theirs. It's clear that the owner of this house won't be home, as they too will be following Winnie-the-Pooh's rule. Consequently, there will be no one to shout "Hooray!" or celebrate the guests. If it happens that multiple houses are equidistant from a character, they will choose to visit the house with the smallest number. Your task is to determine which characters will gather at each house.
Input
The first line contains the number of characters N (2 ≤ N ≤ 100000). Each of the following N lines contains two numbers representing the coordinates of the point on the plane where the corresponding character's house is located. All coordinates are non-negative integers that do not exceed 10^9.
Output
Output N lines. The i-th line should contain the number i, followed by a colon, and then, in ascending order, the numbers of the characters who will come to visit the i-th house.