Square
Given a square at [0, 1]×[0, 1] that has N points ( P_1, P_2, ..., P_N) in the square (you may assume that different points can be at the same position), we can connect the N points and the four corners of the square with some line segments so that through these segments any two of the N+4 points can reach each other (directly or indirectly). The graph length is defined as the total length of the line segments. When N points’ positions are fixed, there must exist a way of connecting them, such that it will make the shortest graph length. We can use LEN (P_1, P_2, ..., P_N) to record the graph length using this way of connecting.
In this situation, LEN (P_1, P_2, ..., P_N) is a function of P_1, P_2, ..., P_N. When P_1, P_2, ..., P_N change their positions, LEN (P_1, P_2, ..., P_N) also changes. It's easy to prove that there exist some P_1', P_2', ..., P_N' in the square such that LEN (P_1', P_2', ..., P_N') is at its minimum.
Given the initial positions of N points, your task is to find out N points P_1", P_2", ..., P_N" in the square such that |P_1P_1"| + |P_2P_2"| + ... + |P_NP_N"| is minimum and LEN (P_1", P_2", ..., P_N") = LEN (P_1', P_2', ..., P_N'). You are requested to output the value of |P_1P_1"| + |P_2P_2"| + ... + |P_NP_N"|, where |P_iP_i"| is the distance between P_i and P_iP_i".
For example, Figure-1 gives the initial position of P_1 and the way of connecting to obtain LEN (P_1). In Figure-2, it gives the position of P_1", which is at the center of the square, and the way of connecting to obtain LEN (P_1"). It can be proved that LEN (P_1") = LEN (P_1'); your job is to output the distance between P_1 and P_1".
Input
The input consists of several test cases. For each test case, the first line consists of one integer N (1 ≤ N ≤ 100), the number of points, and N lines follow to give the coordinates for every point in the following format:
x y
Here, x and y are float numbers within the value [0, 1].
A test case of N = 0 indicates the end of input, and should not be processed.
Output
For each test case, output the value of |P_1P_1"| + |P_2P_2"| + ... + |P_NP_N"|. The value should be rounded to three digits after the decimal point.