Resistance#766

Resistance

1 second

64 megabytes

Easy

A resistor with resistance $r_{1}$ r_1 is connected in series with a resistor of resistance $r_{2}$ r_2. Then another resistor with resistance $r_{1}$ r_1 is connected in parallel to the resulting circuit. After that, a resistor with resistance $r_{2}$ r_2 is again connected in series, and the process continues in the same manner.

In total, the circuit contains $n$ resistors.

Determine the equivalent resistance of the resulting circuit.

Input

Three integers $n, r_{1}, r_{2} (1 \leq n < 2^{31}, 1 \leq r_{1}, r_{2} \leq 5000)$ n, r_1, r_2~(1 \le n < 2^{31},\ 1 \le r_1, r_2 \le 5000).

Output

Print the total resistance of the circuit with precision $1 0^{- 6}$ 10^{-6}.

Examples

Example 1