Jack is upgrading his PC, and he has only one component left to buy, the most important of all, the CPU. Jack doesn't care about the price - all he cares about is raw processing power. Jack has been given a list of CPU specs, containing their clock speed at 1V, and the maximum voltage that a CPU can be run at. Given that a CPU's clock changes in proportion to the voltage, help Jack determine the most powerful CPU.

Input

The first line contains a single integer ~N~ (~1\leq N\leq10^6~) - the number of processors that Jack is considering.

The next line contains integers ~C_1\ \dots\ C_N~ ( ~0\leq C_i \leq10^8~) - ~C_i~ is the clock speed of the ~i~th processor.

The final line contains decimal numbers ~V_1\ \dots\ V_N~ ( ~0.0 \leq V_i\leq 10.0~) - ~V_i~ is the maximum voltage of the ~i~th processor.

Output

Output a single number ~M~ - the maximum clock speed Jack can produce, to 3 decimal places

Example

Input 1

4
3 8 2 6
1.5 2.3 5.9 1.8

Output 1

18.400

~9 \times 2.3 = 18.4~

Input 2

4
6 6 8 7
3.11 6.65 5.35 3.88

Output 2

42.800