Maximize Protected Population with One-Step-Left Move Units

Problem There are n cities in a line, indexed 1..n. City i has population population[i]. You are also given an array unit[i] of length n (0/1), where unit[i] = 1 means city i initially has exactly one security unit, otherwise none. You may reassign units under the following rules: Each security unit can move at most one step to the left (from city i to city i-1), or stay. Each unit can be moved at most once. A unit in city 1 cannot move left. A city is considered protected if it ends up with at least one unit (extra units do not increase the protected value). Goal: maximize the sum of populations of protected cities after moving/staying units under the rules. Input (stdin) Line 1: integer n Line 2: n integers population[1..n] Line 3: n integers unit[1..n] (0/1) Output (stdout) One integer: the maximum possible protected population sum Constraints 1 <= n <= 2e5 0 <= population[i] <= 1e9 unit[i] ∈ {0,1} Example Input: 5 10 5 7 6 12 0 1 0 1 0 Output: 23 Example Input 5 10 5 7 6 12 0 1 0 1 0 Output 23