Currency Manipulations#818
Peter is analyzing how the exchange rate of the hryvnia changes relative to the dollar and the euro, and he believes he has discovered the law governing these changes. Based on this law, Peter has calculated what the exchange rate of the hryvnia to the dollar and the euro will be for the next days.
Peter has hryvnias. Each day, he can exchange currencies with no limit on the amount according to the current rate (the exchange rate between the dollar and euro is given by converting dollars to hryvnias, then those hryvnias to euros). Since Peter operates through a bank account, he can trade any amount, including fractional, of any currency.
Write a program that computes the maximum number of hryvnias Peter can have at the end of the -th day.
The laws of exchange rate changes are set so that during this period, the hryvnia equivalent of what Peter can obtain will not exceed 10^8 hryvnias.
The first line contains a single integer (1 \leq N \leq 5000). The following lines each contain numbers computed according to Peter's law for the given day: how many hryvnias will be the cost of dollar and how many hryvnias will be the cost of euro. All of these values are not less than and not more than . They are given precisely, as real numbers, with at most two digits after the decimal point.
Print the sought value with exactly two decimal places.
Example 1