In English, we have a concept called root, which can be followed by some other word to form another longer word - let's call this word successor. For example, when the root "an" is followed by the successor word "other", we can form a new word "another".

Given a dictionary consisting of many roots and a sentence consisting of words separated by spaces, replace all the successors in the sentence with the root forming it. If a successor can be replaced by more than one root, replace it with the root that has the shortest length.

Return the sentence after the replacement.

Example 1:

Input: dictionary = ["cat","bat","rat"], sentence = "the cattle was rattled by the battery"
Output: "the cat was rat by the bat"

Example 2:

Input: dictionary = ["a","b","c"], sentence = "aadsfasf absbs bbab cadsfafs"
Output: "a a b c"

Constraints:

1 <= dictionary.length <= 1000
1 <= dictionary[i].length <= 100
dictionary[i] consists of only lower-case letters.
1 <= sentence.length <= 10⁶
sentence consists of only lower-case letters and spaces.
The number of words in sentence is in the range [1, 1000]
The length of each word in sentence is in the range [1, 1000]
Every two consecutive words in sentence will be separated by exactly one space.
sentence does not have leading or trailing spaces.

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