#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<map>
#define fo(i,j,k) for(int i=j;i<=k;++i)
#define fd(i,j,k) for(int i=j;i>=k;--i)
using namespace std;
const int N=1e5+10;
int a[N],b[N],f[N];
map<int,int> mp;
int tot=0;
int find(int x){
	return f[x]==x?x:f[x]=find(f[x]);
}
void mg(int x,int y){
	int fx=find(x),fy=find(y);
	if(fx!=fy) f[fy]=fx;
}
int c[N],d[N];
bool check(int n){
	memcpy(c,a,sizeof(c)),memcpy(d,b,sizeof(b));
	sort(c+1,c+n+1),sort(d+1,d+n+1);
	fo(i,1,n) if(c[i]!=d[i]) return false;
	return true;
}
int main()
{
	int n,ans=0;
	scanf("%d",&n);
	fo(i,1,n) scanf("%d",&a[i]),a[n+1]^=a[i];
	fo(i,1,n) scanf("%d",&b[i]),b[n+1]^=b[i];
	n++;
	fo(i,1,n)
	if(a[i]!=b[i] || i==n){
		ans+=i<n;
		if(!mp[a[i]]) mp[a[i]]=++tot;
		if(!mp[b[i]]) mp[b[i]]=++tot;
	}
	if(!check(n)) return printf("-1"),0;
	fo(i,1,tot) f[i]=i;
	fo(i,1,n) if(a[i]!=b[i]) mg(mp[a[i]],mp[b[i]]);
	fo(i,1,tot) if(f[i]==i) ans++;
	printf("%d",ans-1);
}

### Prompt

Develop a solution in Cpp to the problem described below:

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<cstdlib>
#include<cstring>
#include<algorithm>
#include<map>
#define fo(i,j,k) for(int i=j;i<=k;++i)
#define fd(i,j,k) for(int i=j;i>=k;--i)
using namespace std;
const int N=1e5+10;
int a[N],b[N],f[N];
map<int,int> mp;
int tot=0;
int find(int x){
	return f[x]==x?x:f[x]=find(f[x]);
}
void mg(int x,int y){
	int fx=find(x),fy=find(y);
	if(fx!=fy) f[fy]=fx;
}
int c[N],d[N];
bool check(int n){
	memcpy(c,a,sizeof(c)),memcpy(d,b,sizeof(b));
	sort(c+1,c+n+1),sort(d+1,d+n+1);
	fo(i,1,n) if(c[i]!=d[i]) return false;
	return true;
}
int main()
{
	int n,ans=0;
	scanf("%d",&n);
	fo(i,1,n) scanf("%d",&a[i]),a[n+1]^=a[i];
	fo(i,1,n) scanf("%d",&b[i]),b[n+1]^=b[i];
	n++;
	fo(i,1,n)
	if(a[i]!=b[i] || i==n){
		ans+=i<n;
		if(!mp[a[i]]) mp[a[i]]=++tot;
		if(!mp[b[i]]) mp[b[i]]=++tot;
	}
	if(!check(n)) return printf("-1"),0;
	fo(i,1,tot) f[i]=i;
	fo(i,1,n) if(a[i]!=b[i]) mg(mp[a[i]],mp[b[i]]);
	fo(i,1,tot) if(f[i]==i) ans++;
	printf("%d",ans-1);
}

```