2052: [USACO 2025 February Contest, Gold] Problem 1. Bessie's Function

Bessie has a special function f(x) that takes as input an integer in [1, N] and returns an integer in [1, N] (1 ≤ N ≤ 2⋅10⁵). Her function f(x) is defined by N integers a₁…a_N where f(x) = a_x (1 ≤ a_i ≤ N). 

Bessie wants this function to be idempotent. In other words, it should satisfy f(f(x)) = f(x) for all integers x ∈ [1, N]. 

For a cost of c_i, Bessie can change the value of a_i to any integer in [1, N] (1 ≤ c_i ≤ 10⁹). Determine the minimum total cost Bessie needs to make f(x) idempotent.

The second line contains N space-separated integers a₁, a₂, …, a_N.

The third line contains N space-separated integers c₁, c₂, …, c_N.

5
2 4 4 5 3
1 1 1 1 1

3