Meeting Time on a Circular Track

Three friends are running on a circular track with a total length of L units. Friend A, Friend B, and Friend C run with speeds v_A, v_B, and v_C respectively. They start at the same point and run in the same direction. Your task is to compute the time when they will all meet again at a single point on the track.

The meeting time can be computed using the formula:

\( T = \frac{L \times \mathrm{lcm}(v_A, v_B, v_C)}{\gcd(L, \mathrm{lcm}(v_A, v_B, v_C))} \)

Here, \( \mathrm{lcm} \) represents the least common multiple and \( \gcd \) represents the greatest common divisor.

inputFormat

The input consists of a single line containing four space-separated integers: L v_A v_B v_C, where:

• L (1 ≤ L ≤ 10⁹): the total length of the circular track.
• v_A, v_B, v_C (1 ≤ v_i ≤ 10⁹): the speed of each friend.

outputFormat

Output a single floating-point number denoting the time when all three friends meet at one point. The answer should be computed exactly according to the given formula.

12 3 2 1

12.0