Given a pattern and a string str, find if str 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 str.

Examples:
pattern = "abba", str = "dog cat cat dog" should return true.
pattern = "abba", str = "dog cat cat fish" should return false.
pattern = "aaaa", str = "dog cat cat dog" should return false.
pattern = "abba", str = "dog dog dog dog" should return false.

Notes:
You may assume pattern contains only lowercase letters, and str contains lowercase letters separated by a single space.

class Solution(object):
    def wordPattern(self, pattern, str):
        """
        :type pattern: str
        :type str: str
        :rtype: bool
        """
        arr = str.split(" ")
        if len(arr) != len(pattern):
            return False
        f1 = {}
        i = 0
        for x in pattern:
            if x in f1.keys():
                f1[x].append(i)
            else:
                f1[x] = [i];
            i+=1
        
        f2 = {}
        i = 0
        for x in arr:
            if x in f2.keys():
                f2[x].append(i)
            else:
                f2[x] = [i]
            i+=1
        for x in f1.values():
            if x not in f2.values():
                return False
        return True