hewmatt10 is dreaming about [REDACTED]! In his dream, [REDACTED] appears ~N~ times on the 2D plane, at ~N~ different points. Because hewmatt10 likes round objects, all of the ~N~ points appear on an ellipse centred at ~(0, 0)~ with its semi-major and semi-minor axes lying on the x and y-axes, respectively. hewmatt10 wants to be really close to [REDACTED], so he would like to find the distance between the 2 closest points. Can you help hewmatt10?

Input Specification

The first line will contain ~N~. The next ~N~ lines will contains 2 real numbers ~x, y\ (-10^6 \le x, y \le 10^6)~, the coordinates of one of the points.

Output Specification

The distance between the 2 closest points. Your answer will be judged as correct if it is within an absolute or relative error of ~10^{-6}~.

Subtasks

Subtask 1 [30%]

~2 \le N \le 10^3~

Subtask 2 [70%]

~2 \le N \le 2 \cdot 10^5~

Sample Input

10
52.971372 -46.163430
48.437918 -48.556681
-60.234919 -41.540429
-63.111931 39.377980
-24.842362 56.659883
79.122941 20.681073
-11.977885 58.684788
-83.596602 8.292359
32.146228 -54.818804
-83.759327 7.438750

Sample Output

0.868981