#include<bits/stdc++.h>
int n,a[100007],b[100007],as[100007],ap=0;
int f[100007],sz[100007],deg[100007];
int gf(int x){
	while(x!=f[x])x=f[x]=f[f[x]];
	return x;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",a+i),a[0]^=a[i],as[ap++]=a[i];
	for(int i=1;i<=n;++i)scanf("%d",b+i),b[0]^=b[i];
	as[ap++]=a[0];
	std::sort(as,as+ap);
	ap=std::unique(as,as+ap)-as;
	for(int i=0;i<ap;++i)f[i]=i,sz[i]=0;
	for(int i=0;i<=n;++i)a[i]=std::lower_bound(as,as+ap,a[i])-as;
	for(int i=0;i<=n;++i){
		int x=std::lower_bound(as,as+ap,b[i])-as;
		if(x==ap||as[x]!=b[i])return puts("-1"),0;
		b[i]=x;
	}
	for(int i=0;i<=n;++i)if(a[i]!=b[i]||i==0){
		++deg[a[i]];--deg[b[i]];
		//printf("(%d->%d)",a[i],b[i]);
		int x=gf(a[i]),y=gf(b[i]);
		if(x!=y)f[y]=x,sz[x]+=sz[y];
		++sz[x];
	}
	for(int i=0;i<ap;++i)if(deg[i])return puts("-1"),0;
	int s=0,vv=gf(a[0]);
	for(int i=0;i<ap;++i)if(i==f[i]&&sz[i]){
		s+=sz[i]+1;
		if(i==vv)s-=2;
	}
	printf("%d",s);
	return 0;
}
### Prompt

Your challenge is to write 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>
int n,a[100007],b[100007],as[100007],ap=0;
int f[100007],sz[100007],deg[100007];
int gf(int x){
	while(x!=f[x])x=f[x]=f[f[x]];
	return x;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",a+i),a[0]^=a[i],as[ap++]=a[i];
	for(int i=1;i<=n;++i)scanf("%d",b+i),b[0]^=b[i];
	as[ap++]=a[0];
	std::sort(as,as+ap);
	ap=std::unique(as,as+ap)-as;
	for(int i=0;i<ap;++i)f[i]=i,sz[i]=0;
	for(int i=0;i<=n;++i)a[i]=std::lower_bound(as,as+ap,a[i])-as;
	for(int i=0;i<=n;++i){
		int x=std::lower_bound(as,as+ap,b[i])-as;
		if(x==ap||as[x]!=b[i])return puts("-1"),0;
		b[i]=x;
	}
	for(int i=0;i<=n;++i)if(a[i]!=b[i]||i==0){
		++deg[a[i]];--deg[b[i]];
		//printf("(%d->%d)",a[i],b[i]);
		int x=gf(a[i]),y=gf(b[i]);
		if(x!=y)f[y]=x,sz[x]+=sz[y];
		++sz[x];
	}
	for(int i=0;i<ap;++i)if(deg[i])return puts("-1"),0;
	int s=0,vv=gf(a[0]);
	for(int i=0;i<ap;++i)if(i==f[i]&&sz[i]){
		s+=sz[i]+1;
		if(i==vv)s-=2;
	}
	printf("%d",s);
	return 0;
}
```