Problem:
Score : 1000 points

Problem Statement

There is a sequence of length N: a = (a_1, a_2, ..., a_N).
Here, each a_i is a non-negative integer.

Snuke can repeatedly perform the following operation:

Let the XOR of all the elements in a be x. Select an integer i (1 ≤ i ≤ N) and replace a_i with x.

Snuke's objective is to match a with another sequence b = (b_1, b_2, ..., b_N).
Here, each b_i is a non-negative integer.

Determine whether the objective is achievable, and find the minimum necessary number of operations if the answer is positive.

Constraints

2 ≤ N ≤ 10^5

a_i and b_i are integers.

0 ≤ a_i, b_i < 2^{30}

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N
b_1 b_2 ... b_N

Output

If the objective is achievable, print the minimum necessary number of operations.
Otherwise, print -1 instead.

Sample Input 1

3
0 1 2
3 1 0

Sample Output 1

2

At first, the XOR of all the elements of a is 3.
If we replace a_1 with 3, a becomes (3, 1, 2).

Now, the XOR of all the elements of a is 0.
If we replace a_3 with 0, a becomes (3, 1, 0), which matches b.

Sample Input 2

3
0 1 2
0 1 2

Sample Output 2

0

Sample Input 3

2
1 1
0 0

Sample Output 3

-1

Sample Input 4

4
0 1 2 3
1 0 3 2

Sample Output 4

5

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;

class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        long[] a = new long[N];
        long[] b = new long[N];
        for(int i=0;i<N;++i)a[i] =scan.nextLong();
        for(int i=0;i<N;++i)b[i] =scan.nextLong();
        Map<Long,Integer> countmap = new HashMap<>();
        long x = 0;
        for(int i=0;i<N;++i)x^=a[i];
        countmap.put(x,1);
        for(int i=0;i<N;++i){
            if(!countmap.containsKey(a[i]))countmap.put(a[i],0);
            countmap.put(a[i], countmap.get(a[i])+1);
        }
        for(int i=0;i<N;++i){
            if(!countmap.containsKey(b[i]) || countmap.get(b[i])==0){
                System.out.println(-1);
                return;
            }
            countmap.put(b[i], countmap.get(b[i])-1);
        }
        Map<Long, Deque<Integer>> bNumToIndex = new HashMap<>();
        for(int i=0;i<N;++i){
            if(!bNumToIndex.containsKey(b[i]))bNumToIndex.put(b[i],new ArrayDeque<>());
            bNumToIndex.get(b[i]).add(i);
        }
        int ans =0;
        boolean used[] = new boolean[N];
        int index=0;
        for(int i=0;i<N;++i)if(a[i]==b[i])used[i]=true;
        while(true){
            int nextIndex=-1;
            if(bNumToIndex.containsKey(x)){
                nextIndex=bNumToIndex.get(x).poll();
                while(used[nextIndex] && !bNumToIndex.get(x).isEmpty()){
                    nextIndex = bNumToIndex.get(x).poll();
                }
                if(bNumToIndex.get(x).isEmpty())bNumToIndex.remove(x);
                if(used[nextIndex])nextIndex=-1;
                else used[nextIndex]=true;
            }
            if(nextIndex<0){
                while(index<N &&used[index])++index;
                if(index>=N)break;
                nextIndex=index;
            }
            ++ans;
            x=a[nextIndex];
        }

        System.out.println(ans);
    }
}