Minimum Signal Propagation Time

You are given a village with N houses arranged in a row. The position of each house is given by an integer. When a signal is sent from one house, it takes time equal to the distance (i.e. the absolute difference in position) for the signal to reach another house. Since every house sends a signal simultaneously, the minimum time required for every house to receive a signal from every other house is determined by the two houses that are farthest apart.

In other words, if the positions are given by an array positions, the answer is given by $$\max(positions)-\min(positions)$$ Your task is to compute and output this minimum required time.

inputFormat

The input is given via stdin and consists of two lines:

• The first line contains a single integer N — the number of houses.
• The second line contains N space-separated integers, representing the positions of the houses.

outputFormat

The output should be a single integer printed to stdout — the minimum time required for every house to receive signals from every other house.

4
1 3 6 7

6