Design a Food Rating System

Design a food rating system that can do the following:

*   **Modify** the rating of a food item listed in the system.
*   Return the highest-rated food item for a type of cuisine in the system.

Implement the `FoodRatings` class:

*   `FoodRatings(String[] foods, String[] cuisines, int[] ratings)` Initializes the system. The food items are described by `foods`, `cuisines` and `ratings`, all of which have a length of `n`.
    *   `foods[i]` is the name of the `ith` food,
    *   `cuisines[i]` is the type of cuisine of the `ith` food, and
    *   `ratings[i]` is the initial rating of the `ith` food.
*   `void changeRating(String food, int newRating)` Changes the rating of the food item with the name `food`.
*   `String highestRated(String cuisine)` Returns the name of the food item that has the highest rating for the given type of `cuisine`. If there is a tie, return the item with the **lexicographically smaller** name.

Note that a string `x` is lexicographically smaller than string `y` if `x` comes before `y` in dictionary order, that is, either `x` is a prefix of `y`, or if `i` is the first position such that `x[i] != y[i]`, then `x[i]` comes before `y[i]` in alphabetic order.

**Example 1:**

**Input**
\[ "FoodRatings ",  "highestRated ",  "highestRated ",  "changeRating ",  "highestRated ",  "changeRating ",  "highestRated "\]
\[\[\[ "kimchi ",  "miso ",  "sushi ",  "moussaka ",  "ramen ",  "bulgogi "\], \[ "korean ",  "japanese ",  "japanese ",  "greek ",  "japanese ",  "korean "\], \[9, 12, 8, 15, 14, 7\]\], \[ "korean "\], \[ "japanese "\], \[ "sushi ", 16\], \[ "japanese "\], \[ "ramen ", 16\], \[ "japanese "\]\]
**Output**
\[null,  "kimchi ",  "ramen ", null,  "sushi ", null,  "ramen "\]

**Explanation**
FoodRatings foodRatings = new FoodRatings(\[ "kimchi ",  "miso ",  "sushi ",  "moussaka ",  "ramen ",  "bulgogi "\], \[ "korean ",  "japanese ",  "japanese ",  "greek ",  "japanese ",  "korean "\], \[9, 12, 8, 15, 14, 7\]);
foodRatings.highestRated( "korean "); // return  "kimchi "
                                    //  "kimchi " is the highest rated korean food with a rating of 9.
foodRatings.highestRated( "japanese "); // return  "ramen "
                                      //  "ramen " is the highest rated japanese food with a rating of 14.
foodRatings.changeRating( "sushi ", 16); //  "sushi " now has a rating of 16.
foodRatings.highestRated( "japanese "); // return  "sushi "
                                      //  "sushi " is the highest rated japanese food with a rating of 16.
foodRatings.changeRating( "ramen ", 16); //  "ramen " now has a rating of 16.
foodRatings.highestRated( "japanese "); // return  "ramen "
                                      // Both  "sushi " and  "ramen " have a rating of 16.
                                      // However,  "ramen " is lexicographically smaller than  "sushi ".

**Constraints:**

*   `1 <= n <= 2 * 104`
*   `n == foods.length == cuisines.length == ratings.length`
*   `1 <= foods[i].length, cuisines[i].length <= 10`
*   `foods[i]`, `cuisines[i]` consist of lowercase English letters.
*   `1 <= ratings[i] <= 108`
*   All the strings in `foods` are **distinct**.
*   `food` will be the name of a food item in the system across all calls to `changeRating`.
*   `cuisine` will be a type of cuisine of **at least one** food item in the system across all calls to `highestRated`.
*   At most `2 * 104` calls **in total** will be made to `changeRating` and `highestRated`.