Given a pattern and a string s, find if s follows the same pattern.

Here follow means a full match, such that there is a bijection between a letter in pattern and a non-empty word in s. Specifically:

• Each letter in pattern maps to exactly one unique word in s.
• Each unique word in s maps to exactly one letter in pattern.
• No two letters map to the same word, and no two words map to the same letter.

Example 1:

• Input: pattern = “abba”, s = “dog cat cat dog”
• Output: true
• Explanation:
• The bijection can be established as:
• ‘a’ maps to “dog”.
• ‘b’ maps to “cat”.

Example 2:

• Input: pattern = “abba”, s = “dog cat cat fish”
• Output: false

Example 3:

• Input: pattern = “aaaa”, s = “dog cat cat dog”
• Output: false

Constraints:

• 1 <= pattern.length <= 300
• pattern contains only lower-case English letters.
• 1 <= s.length <= 3000
• s contains only lowercase English letters and spaces ‘ ‘.
• s does not contain any leading or trailing spaces.
• All the words in s are separated by a single space.