#include<cstdio>
#include<map>
#include<algorithm>
#define maxn 100005
using namespace std;
int n,a[maxn],b[maxn],fa[maxn],siz[maxn],x,ans,cnt;
map<int,int> mp,val;
int find(int x)
{
	if(fa[x]==x) return x;
	return fa[x]=find(fa[x]);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) fa[i]=i,siz[i]=1;
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		x^=a[i]; mp[a[i]]++;
		if(!val[a[i]]) val[a[i]]=++cnt;
	}
	mp[x]++;
	for(int i=1;i<=n;i++) scanf("%d",&b[i]);
	for(int i=1;i<=n;i++)
	{
		if(!mp[b[i]]) { printf("-1\n"); return 0; }
		mp[b[i]]--;
		if(!val[b[i]]) val[b[i]]=++cnt;
		if(b[i]!=a[i])
		{
			int r1=find(val[a[i]]),r2=find(val[b[i]]);
			if(r1!=r2) fa[r2]=r1,siz[r1]+=siz[r2];
			ans++;
		}
	}
	bool f=true;
	for(int i=1;i<=n;i++) 
		if(a[i]!=b[i]) { f=false; break; }
	if(f) { printf("0\n"); return 0; }
	if(!val[x]) ans++;
	for(int i=1;i<=cnt;i++)
		if(find(i)==i&&siz[i]>1) ans++;
	printf("%d\n",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<map>
#include<algorithm>
#define maxn 100005
using namespace std;
int n,a[maxn],b[maxn],fa[maxn],siz[maxn],x,ans,cnt;
map<int,int> mp,val;
int find(int x)
{
	if(fa[x]==x) return x;
	return fa[x]=find(fa[x]);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) fa[i]=i,siz[i]=1;
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		x^=a[i]; mp[a[i]]++;
		if(!val[a[i]]) val[a[i]]=++cnt;
	}
	mp[x]++;
	for(int i=1;i<=n;i++) scanf("%d",&b[i]);
	for(int i=1;i<=n;i++)
	{
		if(!mp[b[i]]) { printf("-1\n"); return 0; }
		mp[b[i]]--;
		if(!val[b[i]]) val[b[i]]=++cnt;
		if(b[i]!=a[i])
		{
			int r1=find(val[a[i]]),r2=find(val[b[i]]);
			if(r1!=r2) fa[r2]=r1,siz[r1]+=siz[r2];
			ans++;
		}
	}
	bool f=true;
	for(int i=1;i<=n;i++) 
		if(a[i]!=b[i]) { f=false; break; }
	if(f) { printf("0\n"); return 0; }
	if(!val[x]) ans++;
	for(int i=1;i<=cnt;i++)
		if(find(i)==i&&siz[i]>1) ans++;
	printf("%d\n",ans-1);
}
```