Equality Equations

Each string in equations has the form "a==b" or "a!=b", where a and b are single lower-case letters (variables). Return True if you can give each variable an integer so that all equations hold.

For ["a==b", "b!=a"] the answer is False; for ["a==b", "b==c", "a==c"] it is True.

Examples

Example 1

Input:

equations_possible(['a==b', 'b!=a'])

Output:

False

Example 2

Input:

equations_possible(['a==b', 'b==c', 'a==c'])

Output:

True

Constraints

• 0 <= len(equations) <= 100000
• Each equation is 4 characters: a letter, == or !=, a letter.