Description

When doing chemistry problems, Xiao F always miscalculates the relative molecular mass, which makes him very distressed.

Xiao F came to you for help. Please compute the relative molecular mass of the given substance.

If you have not studied the related content, that is fine. You can understand what is required from the samples and the hints.

Input Format

Input consists of one line: a string of length $L$ $(L \leq 100)$ without spaces, representing the chemical formula of the given substance.

The chemical formula includes only the following:

• Elements: such as Au (gold), Hf (hafnium). All occurring elements and their relative atomic masses are given in the appendix.
• Subscript _{}: indicates the count of some atom, ion, or group. For example, H_{2}O means $\text{H}_2\text{O}$ (water), and C_{60} means $\text{C}_{60}$ (buckminsterfullerene).
• Parentheses (): indicate a group, and a subscript applies to the content inside the group. For example, Ca(OH)_{2} means $\text{Ca(OH)}_2$ (slaked lime).
• Hydrate ~: for example, CuSO_{4}~5H_{2}O means $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$ (chalcanthite). If there is a number before water, it is guaranteed to be a positive integer greater than $2$. If this part is omitted, it defaults to $1$. In the example above, the 5 indicates the number of water molecules.

Formally, the chemical formula you process satisfies the following rules:

Molecule ~ Count H_{2}O

The count or the hydrate part may be omitted.

For the molecule, it satisfies:

Part _{ Count } Part _{ Count } ... Part _{ Count }

The count may be omitted.

For each “Part” (atom, group, ion, etc.), it satisfies:

Element

or

( Element _{ Count } Element _{ Count } ... Element _{ Count })

The count may be omitted.

Please note that chemical formulas satisfying the above conditions will not contain nested parentheses. The number referred to as “Count” above does not exceed $10000$.

Output Format

Output one line containing either an integer or a real number whose fractional part is .5, which is your computed result.

It is guaranteed that the result does not exceed $10000$.

Au

197

HfO_{2}

210.5

Ca(OH)_{2}

74

CuSO_{4}~5H_{2}O

250

KAl(SO_{4})_{2}~12H_{2}O

474

Hint

Sample explanations

Gold $\text{Au} : 197$.

Hafnium dioxide $\text{HfO}_2: 178.5 + 2 \times 16 = 210.5$.

Calcium hydroxide (slaked lime) $\text{Ca(OH)}_2 : 40 + (1 + 16) \times 2 = 74$.

Copper(II) sulfate pentahydrate (chalcanthite) $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}: 64 + 32 + 16 \times 4 + 5 \times (1 \times 2 + 16) = 250$.

Potassium aluminum sulfate dodecahydrate (alum) $\text{KAl(SO}_4)_2 \cdot 12\text{H}_2\text{O}$ (Indeed, $474$ is correct.).

Appendix: Possible relative atomic masses

Tips

If you have not studied the related content, the following may help:

zcy teaches you how to compute relative molecular mass

1. Each element starts with an uppercase letter.
2. To compute the molecular mass, multiply the number of occurrences of each atom by its relative atomic mass and sum them up.
3. ~( $\cdot$ ) is equivalent to addition.
4. A subscript is equivalent to multiplication.

Translated by ChatGPT 5