### Problem Statement

Each element of recipe has the form (quotes for clarity) "Amount Ingredient" where Amount is a positive integer. For example, "4 SUGAR" means the recipe calls for 4 units of SUGAR. Return what fraction of the total recipe is accounted for by the elements of ingredients (see examples for further clarifications).

### Definition

 Class: RecipeFraction Method: getFraction Parameters: String[], String[] Returns: double Method signature: double getFraction(String[] recipe, String[] ingredients) (be sure your method is public)

### Notes

-The return value must be within 1e-9 absolute or relative error of the actual result.

### Constraints

-ingredients will contain between 1 and 50 elements inclusive.
-Each element of ingredients will contain between 1 and 50 characters inclusive.
-Each element of ingredients will contain only uppercase letters ('A'-'Z').
-Each element of ingredients will be distinct.
-recipe will contain between 1 and 50 elements inclusive.
-Each element of recipe will contain between 3 and 50 characters inclusive.
-Each element of recipe will have the format (quotes for clarity) "Amount Ingredient" where Amount is an integer with no leading zeros between 1 and 10 inclusive, and Ingredient is a positive length string of uppercase letters.
-Each Ingredient in recipe will be distinct.

### Examples

0)

 ```{"2 GRAPES", "1 APPLES", "3 STRAWBERRIES"}``` `{"APPLES"}`
`Returns: 0.16666666666666666`
 The recipe requires 2+1+3 = 6 total units. APPLES account for 1/6 of the total.
1)

 ```{"2 GRAPES", "1 APPLES", "3 STRAWBERRIES"}``` `{"GRAPES"}`
`Returns: 0.3333333333333333`
 GRAPES account for 2/6 of the total recipe.
2)

 ```{"2 GRAPES", "1 APPLES", "3 STRAWBERRIES"}``` `{"FROGS"}`
`Returns: 0.0`
 There are no FROGS in our recipe.
3)

 `{"1 A","1 B","1 C","5 D","4 E"}` `{"A","E"}`
`Returns: 0.4166666666666667`
 The recipe requires 1+1+1+5+4=12 total units. A and E account for 1+4=5 of these 12.
4)

 `{"9 A","1 B","10 C","5 D","4 E"}` `{"A","B","F"}`
`Returns: 0.3448275862068966`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4638

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=8026&pm=4638