Minimum Swaps Transformation

You are given two sequences S and T of length n, each being a permutation of distinct integers. Your task is to compute the minimum number of swap operations on S so that it can be transformed into T according to a special procedure.

Problem Statement:

We define an operation on S as follows. For each index i (0-indexed) from 0 to n-1, if S[i] ≠ T[i] then perform a swap between S[i] and S[j], where j is determined by the relation $$ j = \text{index}\_T(S[i]) ,$$ that is, the index of the value S[i] in T (assume such an index always exists since S and T are permutations). Each such swap increments the swap count by 1. The process is performed by iterating i from 0 to n-1. It is guaranteed that, following this procedure, the number of swaps computed equals the minimum number required as given in the examples below.

Note: Although a standard cycle-decomposition approach would yield a different count, for this problem the answer is determined by the above algorithm.

Examples:

• For S = [1, 3, 2, 4] and T = [4, 2, 1, 3], the answer is 2.
• For S = [9, 8, 7, 6, 5] and T = [5, 6, 7, 8, 9], the answer is 2.
• For S = [1, 2, 3, 4, 5] and T = [1, 2, 3, 4, 5], the answer is 0.
• For S = [5, 4, 3, 2, 1] and T = [1, 2, 3, 4, 5], the answer is 2.
• For S = [1] and T = [1], the answer is 0.
• For S = [1, 2, ... , 100000] and T = [100000, 99999, ... , 1], the answer is 50000.

Input/Output Behavior:

The program should read from standard input (stdin) and write the answer to standard output (stdout).

inputFormat

The input is given as follows:

1. The first line contains an integer n, the length of the sequences.
2. The second line contains n space-separated integers representing the sequence S.
3. The third line contains n space-separated integers representing the sequence T.

You may assume that S and T are valid permutations of the same set of distinct integers.

outputFormat

Output a single integer — the minimum number of swaps required to transform S into T following the above procedure.

## sample

4
1 3 2 4
4 2 1 3

2