B. Black Cells
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a strip divided into cells, numbered from left to right from $$$0$$$ to $$$10^{18}$$$. Initially, all cells are white.

You can perform the following operation: choose two white cells $$$i$$$ and $$$j$$$, such that $$$i \ne j$$$ and $$$|i - j| \le k$$$, and paint them black.

A list $$$a$$$ is given. All cells from this list must be painted black. Additionally, at most one cell that is not in this list can also be painted black. Your task is to determine the minimum value of $$$k$$$ for which this is possible.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2000$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 < a_i < 10^{18}$$$; $$$a_i < a_{i + 1}$$$).

Additional constraint on the input: the sum of $$$n$$$ across all test cases does not exceed $$$2000$$$.

Output

For each test case, print a single integer — the minimum value of $$$k$$$ for which it is possible to paint all the given cells black.

Example
Input
4
2
1 2
1
7
3
2 4 9
5
1 5 8 10 13
Output
1
1
2
3
Note

In the first example, with $$$k=1$$$, it is possible to paint the cells $$$(1, 2)$$$.

In the second example, with $$$k=1$$$, it is possible to paint the cells $$$(7, 8)$$$.

In the third example, with $$$k=2$$$, it is possible to paint the cells $$$(2, 4)$$$ and $$$(8, 9)$$$.

In the fourth example, with $$$k=3$$$, it is possible to paint the cells $$$(0, 1)$$$, $$$(5, 8)$$$ and $$$(10, 13)$$$.