#include<stdio.h>
#include<map>
using namespace std;
int n,ch[1000005],sh[1000005],ans,sum,fa[1000005],tot,mk[1000005];
map <int,int> mp,mmp;
int gf(int p){
	if(fa[p]==p)return p;
	return fa[p]=gf(fa[p]);
}
void mg(int a,int b){
	int fx=gf(a),fy=gf(b);
	if(fx!=fy){
		fa[fx]=fy;
	}
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&sh[i]);sum^=sh[i];mp[sh[i]]++;
	}mp[sum]++;
	for(int i=1;i<=n;i++){
		scanf("%d",&ch[i]);mp[ch[i]]--;
		if(mp[ch[i]]<0){
			ans=-999999999;
		}
		if(sh[i]!=ch[i]){mk[i]=1;
			ans++;
		}
	}
	sh[n+1]=sum;
	for(int i=1;i<=n+1;i++){
		if(mp[sh[i]]>0){
			ch[n+1]=sh[i];break;
		}
	}
	n++;tot=n+n;
	mk[n]=1;
	for(int i=1;i<=n;i++){
		if(!mk[i])continue;
		if(mmp[sh[i]]==0)mmp[sh[i]]=++tot;
		fa[i]=i;fa[i+n]=i+n;
	}
	for(int i=1;i<=tot;i++)fa[i]=i;
	for(int i=1;i<=n;i++){
		if(!mk[i]){
			fa[i]=fa[i+n]=0;
		}
	}
	for(int i=1;i<=n;i++){
		if(sh[i]!=ch[i])mg(i,i+n);
		mg(i,mmp[sh[i]]);mg(i+n,mmp[ch[i]]);
	}
	for(int i=1;i<=tot;i++){
		if(fa[i]==i){//printf("i:%d\n",i);
			ans++;
		}
	}
	ans--;
	if(ans<0)printf("-1");
	else printf("%d",ans);
}
### 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<stdio.h>
#include<map>
using namespace std;
int n,ch[1000005],sh[1000005],ans,sum,fa[1000005],tot,mk[1000005];
map <int,int> mp,mmp;
int gf(int p){
	if(fa[p]==p)return p;
	return fa[p]=gf(fa[p]);
}
void mg(int a,int b){
	int fx=gf(a),fy=gf(b);
	if(fx!=fy){
		fa[fx]=fy;
	}
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&sh[i]);sum^=sh[i];mp[sh[i]]++;
	}mp[sum]++;
	for(int i=1;i<=n;i++){
		scanf("%d",&ch[i]);mp[ch[i]]--;
		if(mp[ch[i]]<0){
			ans=-999999999;
		}
		if(sh[i]!=ch[i]){mk[i]=1;
			ans++;
		}
	}
	sh[n+1]=sum;
	for(int i=1;i<=n+1;i++){
		if(mp[sh[i]]>0){
			ch[n+1]=sh[i];break;
		}
	}
	n++;tot=n+n;
	mk[n]=1;
	for(int i=1;i<=n;i++){
		if(!mk[i])continue;
		if(mmp[sh[i]]==0)mmp[sh[i]]=++tot;
		fa[i]=i;fa[i+n]=i+n;
	}
	for(int i=1;i<=tot;i++)fa[i]=i;
	for(int i=1;i<=n;i++){
		if(!mk[i]){
			fa[i]=fa[i+n]=0;
		}
	}
	for(int i=1;i<=n;i++){
		if(sh[i]!=ch[i])mg(i,i+n);
		mg(i,mmp[sh[i]]);mg(i+n,mmp[ch[i]]);
	}
	for(int i=1;i<=tot;i++){
		if(fa[i]==i){//printf("i:%d\n",i);
			ans++;
		}
	}
	ans--;
	if(ans<0)printf("-1");
	else printf("%d",ans);
}
```