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There are N glasses of different capacities, each of them containing a different amount of a unique kind of juice. Calculate the maximum number of kinds of juice that can be mixed in a single glass.

Rick is really fond of fruit juices, but he is bored of their traditional flavours. Therefore, he has decided to mix as many of them as possible to obtain something entirely new as a result.

He has N glasses, numbered from 0 to N-1, each containing a different kind of juice. The J-th glass has `capacity[J]` units of capacity and contains `juice[J]` units of juice. In each glass there is at least one unit of juice.

Rick want to create a multivitamin mix in one of the glasses. He is going to do it by pouring juice from several other glasses into the chosen one. Each of the used glasses must be empty at the end (all of the juice from each glass has to be poured out).

What is the maximum number of flavours that Rick can mix?

Write a function:

class Solution { public int solution(int[] juice, int[] capacity); }

that, given arrays `juice` and `capacity`, both of size N, returns the maximum number of flavours that Rick can mix in a single glass.

**Examples:**

1. Given `juice` = [10, 2, 1, 1] and `capacity` = [10, 3, 2, 2], your function should return 2. Rick can pour juice from the 3rd glass into the 2nd one.

2. Given `juice` = [1, 2, 3, 4] and `capacity` = [3, 6, 4, 4], your function should return 3. Rick can pour juice from the 0th and 2nd glasses into the 1st one.

3. Given `juice` = [2, 3] and `capacity` = [3, 4], your function should return 1. No matter which glass he chooses, Rick cannot pour juice from the other one into it. The maximum number of flavours in the chosen glass is 1.

4. Given `juice` = [1, 1, 5] and `capacity` = [6, 5, 8], your function should return 3. Rick can mix all juices in the 2nd glass.

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [2..100,000];
- each element of arrays
juiceandcapacityis an integer within the range [1..1,000,000,000];- arrays juice and capacity have the same length, equal to N;
- for each J juice[J] ≤ capacity[J].

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