Suppose that you want to count the number of cases where a prime number is generated when adding 3 numbers among the given numbers. Given an array nums containing numbers as the parameter, write a function solution to return the number of cases where a prime number is generated when adding 3 different numbers among nums.

Constraints

• Length of nums is between 3 and 50.
• Each element of nums is a natural number between 1 and 1,000, and there are no duplicate numbers.

Examples

Example #1
7 can be generated when using [1,2,4].

Example #2
7 can be generated when using [1,2,4].
11 can be generated when using [1,4,6].
13 can be generated when using [2,4,7].
17 can be generated when using [4,6,7].