Dollar Exchange Rate

Problem Background

(This problem omits the MAX_INT+1 numbers.)

Problem Description

Over the next several days, David will study the exchange rate between the US dollar and the German mark. Write a program to help David decide when to buy or sell marks or dollars, so that starting from $100 he can end up with the highest possible value.

Input Format

The first line of the input file is a natural number $N\;(1\le N\le 100)$, the number of days David studies the exchange rate.

The following $N$ lines each contain a natural number $A\;(1\le A\le 1000)$. The $A$ in line $i+1$ is the average exchange rate for day $i+1$, on which David can either use $100$ dollars to buy $A$ marks, or use $A$ marks to buy $100$ dollars.

Output Format

The first and only line of the output file should contain the required amount of money (in dollars, kept to two decimal places).

Note: because of rounding errors in floating-point arithmetic, an answer within $0.05$ dollars of the correct result is considered correct. David must convert all his money back into dollars before the end of the last day.

Sample Input

5
400
300
500
300
250

Sample Output

266.67

Sample Explanation

Day 1 ... changing 100.0000 dollars = 400.0000 marks
Day 2 ... changing 400.0000 marks = 133.3333 dollars
Day 3 ... changing 133.3333 dollars = 666.6666 marks
Day 5 ... changing 666.6666 marks = 266.6666 dollars

Update on 2017/08/18:

1. The correct answer for the sample is $266.67$.
2. Test point $1$ has been changed to the sample.
3. The original SPJ tolerance was $0.01$; according to the problem statement it has been changed back to $0.05$.