#D2013. Flags
Flags
Flags
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
inputFormat
Input
The input is given from Standard Input in the following format:
N x_1 y_1 : x_N y_N
outputFormat
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
样例
5
2 2
2 2
2 2
2 2
2 20