Final Price Calculation

You are given an initial price \( P_0 \) and a series of discounts to apply sequentially. Each discount is either a percentage discount or a fixed discount. For a percentage discount, the discount is given as a percentage \( p \) (with \( 0 \leq p \leq 100 \)) and reduces the current price by \( p\% \). For a fixed discount, a non-negative amount is subtracted directly from the current price.

The computation is as follows:

[ P_{i} = \begin{cases} P_{i-1} - P_{i-1} \times \frac{p}{100} & \text{if discount is percentage}\ P_{i-1} - d & \text{if discount is fixed} \end{cases} ]

If at any point the price becomes negative, treat the final price as \(0.00\). The result should be rounded to two decimal places.

Input constraints:

• The initial price \( P_0 \) is a positive real number.
• For a percentage discount, \( p \) must be within \([0, 100]\).
• For a fixed discount, the discount amount must be non-negative.

If any of these conditions are violated, an error message is expected:

• If \( P_0 \) is not greater than 0, output: Initial price must be > 0
• If a fixed discount is negative, output: Fixed discount must be non-negative
• If a percentage discount is not in the range \( [0, 100] \), output: Percentage discount must be between 0 and 100

inputFormat

The input is read from stdin and has the following format:

<initial_price>
<n>
<discount_type_1> <value_1>
<discount_type_2> <value_2>
... 
<discount_type_n> <value_n>

Here:

• <initial_price> is a floating point number > 0.
• <n> is an integer indicating the number of discounts.
• Each subsequent line represents a discount. The discount type is either P for a percentage discount or F for a fixed discount, followed by its value as a floating point number.

outputFormat

Output the final price to stdout as a floating point number rounded to two decimal places. In case of invalid input as described above, output the corresponding error message.

## sample

100.0
2
P 10
F 5

85.00

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