Given a string of parentheses types and an array of their efficiency ratings, write a function to find the most efficient valid parentheses sequence that can be formed. Return its total efficiency score.

This problem requires finding the maximum efficiency score of a valid parentheses sequence. A common approach involves dynamic programming. Let dp[i][j] represent the maximum efficiency score for a valid parentheses substring from index i to j. The base cases would be for substrings of length 2. For longer substrings, we can consider splitting the substring at different points k or enclosing a substring i+1 to j-1 within a pair of parentheses. The transitions would involve checking for matching parentheses and summing their efficiencies. The final answer would be dp[0][n-1], where n is the length of the input string.