In an attempt to fix mis-matched parenthesis you attempt all the possible configuration, but you quickly realize how messy it is.

How many distinct valid parentheses permutations are possible for 50 expressions?

**Details and Assumptions**

As an explicit example the number of valid permutations of 4 parentheses is 2: `(( ))`

and `()()`

.

All the opening parentheses have a matching closing parentheses.

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