Swamp
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 h. There are n bumps in the swamp, the i-th bump has coordinates x[i], y[i]. The OX axis is directed parallel to the swamp bank, and the OY 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.
Input
The first line contains numbers h (1 ≤ h ≤ 30000) and n (1 ≤ n ≤ ** 100**). The next n lines contain the coordinates of the points x[i], y[i] (1 ≤ x[i], y[i] ≤ 30000 ). The number h and all coordinates are integers.
Output
Print the length of the minimum jump with 6 decimal digits.