2968：Necklace

There are N points marked on a surface, pair (x_i, y_i) is coordinates of a point number i. Let’s call a necklace a set of N figures which fulfills the following rules.

• The figure #i consists of all such points (x, y) that (x − x_i)² + (y − y_i)² ≤ r_i², where r_i ≥ 0.
• Figures #i and #(i + 1) intersect (1 ≤ i < N)
• Figures #1 and #N intersect
• All the rest pairs of figures do not intersect.

Write a program which takes points and constructs a necklace.

The first line of the input contains one integer number N (2 ≤ N ≤ 100). Each of the next N lines contains two real numbers x_i, y_i (1 000 ≤ x_i, y_i ≤ 1 000), separated by one space. It is guaranteed that at least one necklace exists.

The output has to contain N lines. A line #i contains real number r_i, (0 ≤ r_i < 10 000). To avoid potential accuracy problems, a checking program uses the following rules.

• Figures #i and #j definitely do not intersect if (r_i + r_j) ≤ d_ij − 10⁻⁵
• Figures #i and #j definitely intersect if (d_ij + 10⁻⁵) ≤ (ri + rj).
• The case when d_ij − 10⁻⁵ < (r_i + r_j) < d_ij + 10⁻⁵ is decided in favour of a contestant.
• d_ij equals sqrt((x_i − x_j)² + (y_i − y_j)²) in the rules above.