Append Then Count Lines

Write a function int appendAndCount(const string& filename, const string& line) that:
1. opens filename with an fstream in ios::out | ios::app mode and writes line followed by a newline at the end of the file;
2. closes the stream and reopens the same fstream object on the same file in ios::in mode;
3. counts the lines in the file with a getline loop and returns that count.

The test writes the two lines one and two into the file first, calls appendAndCount("entries_a.txt", "three"), and prints the returned count on its own line (see Expected Output).

Do NOT write a main function.