### Problem Statement

In Chemistry, there's a different meaning to the word 'solution' than in programming. When we mix x liters of some substance with (100-x) liters of water, we get 100 liters of x-% solution of that substance.

You are given several bottles containing solutions of the same substance. The i-th bottle contains amount[i] liters of percent[i]-% solution. Return the maximal number of liters of need-% solution we can get by pouring together some of these bottles (possibly partially, see example 0).

### Definition

 Class: MixingLiquids Method: howMuch Parameters: int[], int[], int Returns: double Method signature: double howMuch(int[] percent, int[] amount, int need) (be sure your method is public)

### Notes

-The returned value must have an absolute or relative error less than 1e-9.

### Constraints

-percent will contain between 1 and 50 elements, inclusive.
-Each element of percent will be between 0 and 100, inclusive.
-amount will contain the same number of elements as percent.
-Each element of amount will be between 1 and 1000, inclusive.
-need will be between 0 and 100, inclusive.

### Examples

0)

 `{0, 100}` `{20, 30}` `50`
`Returns: 40.0`
 We have 20 liters of water and 30 liters of pure substance. We need a 50% solution, so we combine all the water with 20 liters of substance.
1)

 `{0, 100}` `{20, 30}` `60`
`Returns: 50.0`
 We can use everything we have.
2)

 `{90, 70, 80}` `{10, 10, 10}` `50`
`Returns: 0.0`
 All our bottles contain too much substance.
3)

 `{30, 80, 60}` `{40, 10, 15}` `57`
`Returns: 35.18518518518519`
4)

 `{50,50,50}` `{395,971,964}` `50`
`Returns: 2330.0`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=7886

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10712&pm=7886

Petr

#### Testers:

PabloGilberto , brett1479 , Olexiy , marian

Sorting