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.