The frequencies of two sound waves compared using the scale on the screen

Problem Statement

Two different sounds were generated in a laboratory, and the sound waves from each were captured by a microphone and displayed on a computer screen. The screen was marked with vertical grid lines at equal intervals, and the time represented by one grid square was the same for both waves.

When the first sound wave was displayed on the screen, it was found that the length of one cycle of the wave (from one peak to the next) corresponded exactly to $N_1$N1​ grid squares on the screen. Let the frequency of this sound wave be $f_1$f1​. Next, when the second sound wave was displayed on the screen, it was found that the length of one cycle of the wave corresponded exactly to $N_2$N2​ grid squares on the screen. Let the frequency of this sound wave be $f_2$f2​.

The unit of frequency $f$f is hertz ($\mathrm{Hz}$Hz), and the relationship between frequency and period (the time taken for one cycle) $T$T is given by $f = \frac{1}{T}$f=T1​.

Find the difference between the frequencies of the two sound waves ($f_2 - f_1$f2​−f1​), which is the larger frequency minus the smaller one, and determine the natural number that conforms to the following input format.

Constraints

• Time represented by one unit on the screen: $\Delta t = 0.00100\text{ }\mathrm{s}$Δt=0.00100 s
• Number of grid squares in one period of the first wave: $N_1 = 5$N1​=5
• Number of grid squares in one period of the second wave: $N_2 = 2$N2​=2

Input Format

Let $A$A be the numerical value of the difference in frequencies $f_2 - f_1$f2​−f1​. Enter the value of $A$A as a natural number.