### Problem Statement

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:

### Sample Output 1

The optimal solution is to place the first flag at coordinate 1, the second flag at coordinate 5 and the third flag at coordinate 9. The smallest distance between two of the flags is 4 in this case.

### Sample Output 2

There can be more than one flag at the same position.