Flatten Nested Dictionary

You are given a nested dictionary represented in JSON format. Your task is to flatten this dictionary so that all nested keys are concatenated into a single key with each level separated by a dot ('.').

For example, given the dictionary

{"a": 1, "b": {"c": 2, "d": {"e": 3}}, "f": {"g": 4}}

the flattened result should be

{"a": 1, "b.c": 2, "b.d.e": 3, "f.g": 4}

The key concatenation follows the formula below:

$$ key = parent \; key + "." + current \; key $$

If the dictionary is empty or there is no nesting, simply output the dictionary as is.

Input is provided via standard input (stdin) as a single line JSON string and the output should be printed to standard output (stdout) as a JSON string without extra spaces.

inputFormat

The input consists of a single line representing a valid JSON object (dictionary). The keys are strings and the values may be integers or nested dictionaries.

Example:

{"a": 1, "b": {"c": 2, "d": {"e": 3}}, "f": {"g": 4}}

outputFormat

Output a JSON string representing the flattened dictionary. The keys in the flattened dictionary are the paths to the corresponding values in the original dictionary, joined by a dot.

Example:

{"a":1,"b.c":2,"b.d.e":3,"f.g":4}

## sample

{"a": 1, "b": {"c": 2, "d": {"e": 3}}, "f": {"g": 4}}

{"a":1,"b.c":2,"b.d.e":3,"f.g":4}