Word Pattern

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

Here follows 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.

Examples

Example 1:

Input: pattern = "abba", s = "dog cat cat dog"

Output: true

Explanation: The bijection is: 'a' -> "dog", 'b' -> "cat".

Example 2:

Input: pattern = "abba", s = "dog cat cat fish"

Output: false

Explanation: 'a' maps to "dog" at index 0 but would need to map to "fish" at index 3.

Example 3:

Input: pattern = "aaaa", s = "dog cat cat dog"

Output: false

Explanation: 'a' maps to "dog" at index 0 but would need to map to "cat" at index 1.

Constraints

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