Background

Problem Description

Given two $0$-$1$ sequences $a$ and $b$, both of length $n$. First, you may choose some $a_i$ to flip, i.e., change $0$ to $1$ and $1$ to $0$. Then, you may permute sequence $a$ in any order.

After the above process, it is required that $a_i$ equals $b_i$. Find the minimum number of flips.

Input Format

The first line contains a positive integer $n$. The second line contains $n$ numbers representing sequence $a$. The third line contains $n$ numbers representing sequence $b$.

Output Format

Output one integer representing the answer.

3
110
101

0

5
10010
00100

1

Hint

Sample Explanation

Input #1: Reorder $a = 110$ into $a = 101$ to meet the requirement, so the minimum number of flips is $0$.

Input #2: Flip the fourth bit of $a = 10010$ (counting from left to right), obtaining $a = 10000$, then reorder it to get $a = 00100$, which meets the requirement, so the minimum number of flips is $1$.

Constraints

• For $10\%$ of the testdata, $n = 1$.
• For another $20\%$ of the testdata, $b_i = 0$.
• For another $20\%$ of the testdata, $b_i = 1$.
• For $100\%$ of the testdata, $1 \le n \le 10^3$, $a_i \in \{0, 1\}$, $b_i \in \{0, 1\}$.

Translated by ChatGPT 5