#include <bits/stdc++.h>
#define F first
#define S second
#define X real()
#define Y imag()
using namespace std;
typedef long long ll;
typedef long double ld;

int a[101010];
int b[101010];

map<int, vector<int> > g;
map<int, int> u;

void dfs(int x){
	if (u[x]) return;
	u[x]=1;
	for (int nx:g[x]){
		dfs(nx);
	}
}

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	int xa=0;
	map<int, int> ca,cb;
	for (int i=0;i<n;i++){
		cin>>a[i];
		xa^=a[i];
		ca[a[i]]++;
	}
	ca[xa]++;
	int xb=0;
	for (int i=0;i<n;i++){
		cin>>b[i];
		xb^=b[i];
		cb[b[i]]++;
	}
	cb[xb]++;
	for (auto t:ca){
		if (cb[t.F]!=t.S){
			cout<<-1<<endl;
			return 0;
		}
	}
	int fa=0;
	for (int i=0;i<n;i++){
		if (a[i]!=b[i]) {
			fa++;
			g[a[i]].push_back(b[i]);
			g[b[i]].push_back(a[i]);
		}
	}
	int cc=0;
	for (auto& t:g){
		if (!u[t.F]){
			cc++;
			dfs(t.F);
		}
	}
	if (g.count(xa)){
		cc--;
	}
	cout<<fa+cc<<endl;
}
### Prompt

Please formulate a CPP solution to the following problem:

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.

Examples

Input

3
0 1 2
3 1 0


Output

2


Input

3
0 1 2
0 1 2


Output

0


Input

2
1 1
0 0


Output

-1


Input

4
0 1 2 3
1 0 3 2


Output

5

### Response

```cpp
#include <bits/stdc++.h>
#define F first
#define S second
#define X real()
#define Y imag()
using namespace std;
typedef long long ll;
typedef long double ld;

int a[101010];
int b[101010];

map<int, vector<int> > g;
map<int, int> u;

void dfs(int x){
	if (u[x]) return;
	u[x]=1;
	for (int nx:g[x]){
		dfs(nx);
	}
}

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	int xa=0;
	map<int, int> ca,cb;
	for (int i=0;i<n;i++){
		cin>>a[i];
		xa^=a[i];
		ca[a[i]]++;
	}
	ca[xa]++;
	int xb=0;
	for (int i=0;i<n;i++){
		cin>>b[i];
		xb^=b[i];
		cb[b[i]]++;
	}
	cb[xb]++;
	for (auto t:ca){
		if (cb[t.F]!=t.S){
			cout<<-1<<endl;
			return 0;
		}
	}
	int fa=0;
	for (int i=0;i<n;i++){
		if (a[i]!=b[i]) {
			fa++;
			g[a[i]].push_back(b[i]);
			g[b[i]].push_back(a[i]);
		}
	}
	int cc=0;
	for (auto& t:g){
		if (!u[t.F]){
			cc++;
			dfs(t.F);
		}
	}
	if (g.count(xa)){
		cc--;
	}
	cout<<fa+cc<<endl;
}
```