#include<bits/stdc++.h>
using namespace std;

map<int,int>mp;
const int N=200100;
int n,fa[N],a[N],b[N],c[N],d[N],cnt,ans;
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;++i)cin>>a[i],a[0]^=a[i];
	for(int i=1;i<=n;++i)cin>>b[i],b[0]^=b[i];
	for(int i=0;i<=n;++i)c[i]=a[i],d[i]=b[i];
	sort(c,c+n+1);sort(d,d+n+1);
	for(int i=0;i<=n;++i)if(c[i]!=d[i]){
		cout<<-1<<'\n';
		return 0;
	}
	if(!mp.count(a[0]))mp[a[0]]=++cnt,fa[cnt]=cnt;
	for(int i=1;i<=n;++i)
		if(a[i]!=b[i]){
			if(!mp.count(a[i]))mp[a[i]]=++cnt,fa[cnt]=cnt;
			if(!mp.count(b[i]))mp[b[i]]=++cnt,fa[cnt]=cnt;
			int u=mp[a[i]],v=mp[b[i]];
			fa[find(u)]=find(v);
			++ans;
		}
	for(int i=1;i<=cnt;++i)ans+=fa[i]==i;
	cout<<(ans-1)<<'\n';
	return 0;
}

### 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<bits/stdc++.h>
using namespace std;

map<int,int>mp;
const int N=200100;
int n,fa[N],a[N],b[N],c[N],d[N],cnt,ans;
int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;++i)cin>>a[i],a[0]^=a[i];
	for(int i=1;i<=n;++i)cin>>b[i],b[0]^=b[i];
	for(int i=0;i<=n;++i)c[i]=a[i],d[i]=b[i];
	sort(c,c+n+1);sort(d,d+n+1);
	for(int i=0;i<=n;++i)if(c[i]!=d[i]){
		cout<<-1<<'\n';
		return 0;
	}
	if(!mp.count(a[0]))mp[a[0]]=++cnt,fa[cnt]=cnt;
	for(int i=1;i<=n;++i)
		if(a[i]!=b[i]){
			if(!mp.count(a[i]))mp[a[i]]=++cnt,fa[cnt]=cnt;
			if(!mp.count(b[i]))mp[b[i]]=++cnt,fa[cnt]=cnt;
			int u=mp[a[i]],v=mp[b[i]];
			fa[find(u)]=find(v);
			++ans;
		}
	for(int i=1;i<=cnt;++i)ans+=fa[i]==i;
	cout<<(ans-1)<<'\n';
	return 0;
}

```