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.

Example 1

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

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.