B"Based on a peculiar incident at basketball practice, Akari came up with the following competitive programming problem! You are given n points on the plane, no three of which are collinear. The i -th point initially has a label a_i , in such a way that the labels a_1, a_2, ... , a_n form a permutation of 1, 2, ... , n . You are allowed to modify the labels through the following operation: A sequence of operations is valid if after applying all of the operations in the sequence in order, the k -th point ends up having the label k for all k between 1 and n inclusive, and the drawn segments don't intersect each other internally. Formally, if two of the segments intersect, then they must do so at a common endpoint of both segments. In particular, all drawn segments must be distinct. Find any valid sequence of operations, or say that none exist. The first line contains an integer n ( 3 <= n <= 2000 ) -- the number of points. The i -th of the following n lines contains three integers x_i , y_i , a_i ( -10^6 <= x_i, y_i <= 10^6 , 1 <= a_i <= n ), representing that the i -th point has coordinates (x_i, y_i) and initially has label a_i . It is guaranteed that all points are distinct, no three points are collinear, and the labels a_1, a_2, ... , a_n form a permutation of 1, 2, ... , n . If it is impossible to perform a valid sequence of operations, print -1 . Otherwise, print an integer k ( 0 <= k <= frac{n(n - 1)}{2} ) -- the number of operations to perform, followed by k lines, each containing two integers i and j ( 1 <= i, j <= n , i neq j ) -- the indices of the points chosen for the operation. Note that you are not required to minimize or maximize the value of k . If there are multiple possible answers, you may print any of them. The following animation showcases t"...