Back to Intermediate Math

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

You want to cross a river of width $d$ metres. The current flows parallel to the bank at speed $v$ m/s, while the boat's speed relative to the water is $u$ m/s.

There are two objectives:

• Fastest crossing: point the boat perpendicular to the bank so the cross-river component is maximal; the current may carry the boat downstream.
• Shortest path: point the boat upstream just enough that the actual trajectory is perpendicular to the bank.

If these two different crossings are both well-defined, compute the shortest-path time minus the fastest-crossing time. Otherwise report that the value cannot be determined.

Input

One line contains three nonnegative real numbers $d$, $v$, $u$, with $d>0$.

Output

If two different crossings as described cannot be determined, print

can't determine

Otherwise print the time difference with exactly three digits after the decimal point.

Subtasks

• Subtask 1 (20%): Only cases where two distinct crossings cannot be determined.
• Subtask 2 (30%): $d,v,u$ are integers and two distinct crossings exist.
• Subtask 3 (50%): Full source domain: $d>0$, $v\ge0$, $u\ge0$.

Examples

Input

8 5 6

Output

1.079

Explanation

For $d=8$, $v=5$, and $u=6$, the fastest crossing time is

For the path whose actual trajectory is perpendicular to the bank, the cross-river speed is

Hence that crossing time is

The difference is $t_s-t_f\approx1.078758$, which rounds to 1.079.