#include <algorithm>
#include <cstdio>
using namespace std;
const int N=100005;
int a[N],b[N],c[N*2],fa[N];
bool u[N];
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int main(){
	int n,m=0;
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),a[0]^=a[i];
	for (int i=1;i<=n;i++) scanf("%d",&b[i]),b[0]^=b[i];
	for (int i=1;i<=n;i++)
		if (a[i]!=b[i]) a[++m]=a[i],b[m]=b[i];
	n=m;
	for (int i=0;i<=n;i++) c[i]=a[i],c[n+1+i]=b[i];
	sort(c,c+n+1);
	sort(c+n+1,c+n+n+2);
	for (int i=0;i<=n;i++)
		if (c[i]!=c[n+1+i]){
			printf("-1\n");
			return 0;
		}
	m=unique(c,c+n+1)-c-1;
	for (int i=0;i<=m;i++) fa[i]=i;
	for (int i=0;i<=n;i++){
		a[i]=lower_bound(c,c+m+1,a[i])-c;
		b[i]=lower_bound(c,c+m+1,b[i])-c;
		fa[find(a[i])]=find(b[i]);
	}
	int ans=n;
	for (int i=0;i<=m;i++)
		if (find(i)==i) ans++;
	printf("%d\n",ans-1);
}
### Prompt

Please create a solution in Cpp 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 <algorithm>
#include <cstdio>
using namespace std;
const int N=100005;
int a[N],b[N],c[N*2],fa[N];
bool u[N];
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
int main(){
	int n,m=0;
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),a[0]^=a[i];
	for (int i=1;i<=n;i++) scanf("%d",&b[i]),b[0]^=b[i];
	for (int i=1;i<=n;i++)
		if (a[i]!=b[i]) a[++m]=a[i],b[m]=b[i];
	n=m;
	for (int i=0;i<=n;i++) c[i]=a[i],c[n+1+i]=b[i];
	sort(c,c+n+1);
	sort(c+n+1,c+n+n+2);
	for (int i=0;i<=n;i++)
		if (c[i]!=c[n+1+i]){
			printf("-1\n");
			return 0;
		}
	m=unique(c,c+n+1)-c-1;
	for (int i=0;i<=m;i++) fa[i]=i;
	for (int i=0;i<=n;i++){
		a[i]=lower_bound(c,c+m+1,a[i])-c;
		b[i]=lower_bound(c,c+m+1,b[i])-c;
		fa[find(a[i])]=find(b[i]);
	}
	int ans=n;
	for (int i=0;i<=m;i++)
		if (find(i)==i) ans++;
	printf("%d\n",ans-1);
}
```