Solve the programming task below in a Python markdown code block.
Snuke loves flags.

Snuke is placing N flags on a line.

The i-th flag can be placed at either coordinate x_i or coordinate y_i.

Snuke thinks that the flags look nicer when the smallest distance between two of them, d, is larger. Find the maximum possible value of d.

Constraints

* 2 ≤ N ≤ 10^{4}
* 1 ≤ x_i, y_i ≤ 10^{9}
* x_i and y_i are integers.

Input

The input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print the answer.

Examples

Input

3
1 3
2 5
1 9


Output

4


Input

5
2 2
2 2
2 2
2 2
2 2


Output

0


Input

22
93 6440
78 6647
862 11
8306 9689
798 99
801 521
188 206
6079 971
4559 209
50 94
92 6270
5403 560
803 83
1855 99
42 504
75 484
629 11
92 122
3359 37
28 16
648 14
11 269


Output

17