Description

There are N (2<=N<=200,000) real numbers. Find the max interval between the adjacent numbers.

Input

The first line is the number of cases. Following is the cases: Line one: N; Line two: N real numbers.

Output

The output contains a single line with the max interval, rounded to the third decimal.

Sample

Input

1
5
2.3 3.1 7.5 1.5 6.3

Output

3.200

Source: lily