#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define SF scanf
#define PF printf
#define MAXN 100010
using namespace std;
int a[MAXN],b[MAXN],c[MAXN],d[MAXN];
int n,sum;
int fa[MAXN],flag[MAXN];
int get_fa(int x){
	if(fa[x]==0)
		return x;
	fa[x]=get_fa(fa[x]);
	return fa[x];	
}
void merge(int x,int y){
	x=get_fa(x),y=get_fa(y);
	if(x!=y)
		fa[x]=y;
}
int main(){
	SF("%d",&n);
	for(int i=1;i<=n;i++){
		SF("%d",&a[i]);
		sum^=a[i];
	}
	a[n+1]=sum;
	sum=0;
	for(int i=1;i<=n;i++){
		SF("%d",&b[i]);
		sum^=b[i];
	}
	b[++n]=sum;
	for(int i=1;i<=n;i++){
		c[i]=a[i];
		d[i]=b[i];
	}
	sort(c+1,c+1+n);
	sort(d+1,d+1+n);
	for(int i=1;i<=n;i++)
		if(c[i]!=d[i]){
			PF("-1");	
			return 0;
		}
	int ans=0;
	for(int i=1;i<=n;i++)
		if(a[i]!=b[i]||i==n){
			if(i!=n)
				ans++;
			int x=lower_bound(c+1,c+1+n,a[i])-c;
			int y=lower_bound(c+1,c+1+n,b[i])-c;
			flag[x]=flag[y]=1;
			merge(x,y);
		}
	if(ans==0){
		PF("0");
		return 0;	
	}
	for(int i=1;i<=n;i++)
		if(flag[i]&&fa[i]==0)
			ans++;
	PF("%d",ans-1);
}
### 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<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define SF scanf
#define PF printf
#define MAXN 100010
using namespace std;
int a[MAXN],b[MAXN],c[MAXN],d[MAXN];
int n,sum;
int fa[MAXN],flag[MAXN];
int get_fa(int x){
	if(fa[x]==0)
		return x;
	fa[x]=get_fa(fa[x]);
	return fa[x];	
}
void merge(int x,int y){
	x=get_fa(x),y=get_fa(y);
	if(x!=y)
		fa[x]=y;
}
int main(){
	SF("%d",&n);
	for(int i=1;i<=n;i++){
		SF("%d",&a[i]);
		sum^=a[i];
	}
	a[n+1]=sum;
	sum=0;
	for(int i=1;i<=n;i++){
		SF("%d",&b[i]);
		sum^=b[i];
	}
	b[++n]=sum;
	for(int i=1;i<=n;i++){
		c[i]=a[i];
		d[i]=b[i];
	}
	sort(c+1,c+1+n);
	sort(d+1,d+1+n);
	for(int i=1;i<=n;i++)
		if(c[i]!=d[i]){
			PF("-1");	
			return 0;
		}
	int ans=0;
	for(int i=1;i<=n;i++)
		if(a[i]!=b[i]||i==n){
			if(i!=n)
				ans++;
			int x=lower_bound(c+1,c+1+n,a[i])-c;
			int y=lower_bound(c+1,c+1+n,b[i])-c;
			flag[x]=flag[y]=1;
			merge(x,y);
		}
	if(ans==0){
		PF("0");
		return 0;	
	}
	for(int i=1;i<=n;i++)
		if(flag[i]&&fa[i]==0)
			ans++;
	PF("%d",ans-1);
}
```