Molar Mass

Time limit1sMemory limit128 MB

Summary

The program parses each formula of C, H, O, and N with optional atom counts and prints its molar mass using the given weights.

Level: Easy2 of 10
Topics: String, Implementation
Solved: No attempts yet

Problem

An organic compound is any member of a large class of chemical compounds whose molecules contain carbon. The molar mass of an organic compound is the mass of one mole of that compound, and it can be computed from the standard atomic weights of the elements.

Given a molecular formula, Dr. CHON wants to find its molar mass. A molecular formula such as C3H4O3 identifies each constituent element by its chemical symbol and gives the number of atoms of that element in one molecule of the compound. When a molecule contains more than one atom of an element, the count is written as a subscript after the chemical symbol.

In this problem, assume that a molecular formula is made up of only the four elements 'C' (carbon), 'H' (hydrogen), 'O' (oxygen), and 'N' (nitrogen), and contains no parentheses.

The table below gives the standard atomic weights of 'C', 'H', 'O', and 'N'.

Element	Carbon (C)	Hydrogen (H)	Oxygen (O)	Nitrogen (N)
Standard atomic weight	12.01 g/mol	1.008 g/mol	16.00 g/mol	14.01 g/mol

For example, the molar mass of the formula C6H5OH is $6 \times 12.01 + 6 \times 1.008 + 1 \times 16.00 = 94.108$ g/mol. Given a molecular formula, write a program that computes its molar mass.

Input

Your program reads from standard input. The input consists of $T$ test cases. The number of test cases $T$ is given on the first line. Each test case is given on a single line containing one molecular formula as a string. Chemical symbols are given as capital letters, and the length of the string is greater than 0 and less than 80. The count $n$ that follows a chemical symbol is omitted when it is 1; otherwise $2 \le n \le 99$ .

Output

Your program writes to standard output. Print exactly one line for each test case. The line contains the molar mass of the given molecular formula, printed to exactly three decimal places.

Examples4

Example 1

Input

4
C
C6H5OH
NH2CH2COOH
C12H22O11

Expected output

Example 2
Input
```
4
H
O
N
C
```
Expected output
```
1.008
16.000
14.010
12.010
```
Example 3
Input
```
3
H2O
CO2
NH3
```
Expected output
```
18.016
44.010
17.034
```
Example 4
Input
```
1
C8H10N4O2
```
Expected output
```
194.200
```