# Balanced sub-sequence

Consider two strings $$S$$ and $$T$$ of length $$n$$.Here both the strings $$S$$ and $$T$$ consists of only $$“(“$$ and $$“)”$$ that is made of parenthesis. I need to find a string $$w$$ which is balanced parenthesis and it should be sub-sequences of both $$S$$ and $$T$$ among all those strings $$w$$ i need the maximum length strings.

This problem is clearly a dynamic programming problem,but i am having hard time in finding states and also their transitions .Could anyone help me.

P.S – Problem E ,but it is in Russian