Given a convex polygon with $n$ vertices in counter-clockwise order (three points may be collinear), find its diameter.

Input

The first line of the input contains an integer $n$.

The next $n$ lines each contain two integers $x_i, y_i$, describing the coordinates of a point. The coordinates are given in counter-clockwise order.

Output

Output a single real number representing the answer. Your answer will be considered correct if the relative error compared to the standard answer does not exceed $10^{-6}$.

Examples

Input 1

3
0 0
4 0
2 2

Output 1

4

Input 2

4
0 0
1 0
1 1
0 1

Output 2

1.414213562373

Input 3

10
0 0
461074 -72768411
3213786 -131277098
9156758 -204048615
50058801 -267750564
98614697 -289078664
138651620 -243972492
191427505 -152569765
131060323 -88251044
85141546 -55035262

Output 3

305436298.50498565947291157209925

Subtasks

For all data, $3 \leq n \leq 5 \times 10^5$, $-10^9 \le x_i, y_i \le 10^9$.

• Subtask 1 (10 pts): $n \leq 10^3$
• Subtask 2 (30 pts): $n \leq 3 \times 10^4$
• Subtask 3 (60 pts): No additional constraints.