Minimize Farthest Travel Distance

Given the coordinates of houses, each represented by a pair of integers (x, y), determine the maximum Euclidean distance from the origin (0, 0) among all houses. In other words, if the distance to a house is computed as \(d = \sqrt{x^2 + y^2}\), find \(\max\{d\}\) across all given houses. The answer must be rounded to six decimal places.

This problem simulates a delivery plan where the goal is to minimize the distance to the farthest house by choosing an optimal starting point, which in this simplified model is always the origin.

Constraints: The number of houses \(n\) is at least 1, and the absolute values of \(x\) and \(y\) can be as large as \(10^9\).

inputFormat

The first line contains an integer \(n\) denoting the number of delivery requests.

The next \(n\) lines each contain two space-separated integers \(x\) and \(y\), representing the coordinates of a house.

outputFormat

Output a single floating-point number representing the maximum distance (i.e. the minimized farthest travel distance) from the origin among the provided houses, rounded to six decimal places.

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5.000000