Swamp#5140
Ivan Tsarevich wants to save Vasilisa the Beautiful from the dungeon. On the way to the dungeon where Koschey the Deathless holds the prisoner, there is a swamp with parallel infinitely long banks of width . There are bumps in the swamp, the -th bump has coordinates x_i, y_i. The axis is directed parallel to the swamp bank, and the axis is directed perpendicular to the swamp bank from the initial bank to the final one, the points of the initial bank have the coordinate y = 0.
Determine what is the minimum length of the jump that Ivan Tsarevich must have in order to cross the swamp.
The first line contains numbers (1 \leq h \leq 30000) and (1 \leq n \leq 100). The next lines contain the coordinates of the points x_i, y_i (1 \leq x_i, y_i \leq 30000). The number and all coordinates are integers.
Print the length of the minimum jump with decimal digits.
\begin{example}\exmp{5 22 24 3}{3.605551}%\end{example}
Example 1
Example 2