A bracket sequence is a string containing only characters "(" and ")".

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()()", "(())" are regular (the resulting expressions are: "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.

You are given $n$ bracket sequences $s_1,s_2,\dots ,s_n$. Calculate the number of pairs $i,j(1\le i,j\le n)$ such that the bracket sequence $s_i+s_j$ is a regular bracket sequence. Operation $+$ means concatenation i.e. "()(" + ")()" = "()()()".

If $s_i+s_j$ and $s_j+s_i$ are regular bracket sequences and $i$