#00003B

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The government of the land of Baitovia wants to connect all the villages in the area with a wireless network. It will use two types of wireless communication: every village will have an identical radio transmitter/emitter, but in addition to this some villages will have a radio antenna. Two villages that have both have a satellite antenna can communicate using the satellite no matter how far apart they are from each other. Two villages can communicate with radio transmitters only if they are not separated by a distance greater than distance D. Distance D depends on the power of the radio transmitter. To decrease the losses of building a wireless network, thegovernment wants to buy radio transmitters that have less power.


You need to calculate the minimum distance D that enables all the villages to be connected (directly or indirectly) with radio transmitters or satellites.


InputThe first line of the standard input contains two integers S ( 2 <= S <= 20 ), which is the number of satellite antennas, and N (N <= 200), which represents the number of villages. In the following N lines there are two integers xi and yi (0 <= xi , yi <= 10 000) that represent the coordinates of the i-th village.

OutputTo the first line of the standard output write the minimum distance D as a real number to two decimal places.

Input:
2 4
0 100
0 300
0 600
150 750

Output:
212.13

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