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Target Sum Subsets - Dp

1. You are given a number n, representing the count of elements. 2. You are given n numbers. 3. You are given a number "tar". 4. You are required to calculate and print true or false, if there is a subset the elements of which add up to "tar" or not.

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Target Sum Subsets - Dp

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1. You are given a number n, representing the count of elements. 2. You are given n numbers. 3. You are given a number "tar". 4. You are required to calculate and print true or false, if there is a subset the elements of which add up to "tar" or not.

Constraints

1 <= n <= 30 0 <= n1, n2, .. n elements <= 20 0 <= tar <= 50

Format

Input

A number n n1 n2 .. n number of elements A number tar

Output

true or false as required

Example

Sample Input

5 4 2 7 1 3 10

Sample Output

true

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