#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
int n,a[N],b[N],id;
vector<int> e[N];
map<int,int> M;
bool vis[N];
void dfs(int x){
	vis[x]=1;
	for (int i=0;i<e[x].size();i++)
	if (!vis[e[x][i]]) dfs(e[x][i]);
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),a[0]^=a[i];
	for (int i=1;i<=n;i++) scanf("%d",&b[i]),b[0]^=b[i];
	for (int i=0;i<=n;i++) M[a[i]]++,M[b[i]]--;
	for (int i=0;i<=n;i++)
		if (M[a[i]]) return puts("-1"),0;
	for (int i=0;i<=n;i++)
		if (!M[a[i]]) M[a[i]]=++id;
	int ans=0;
	for (int i=0;i<=n;i++)
		if (a[i]!=b[i]) e[M[a[i]]].push_back(M[b[i]]),ans++;
	for (int i=1;i<=id;i++)
		if (!vis[i]&&!e[i].empty()) dfs(i),ans++;
	if (!e[M[a[0]]].empty()) ans--;
	if (a[0]!=b[0]) ans--;
	printf("%d\n",ans);
	return 0;
}

### Prompt

Please create a solution in Cpp 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>
using namespace std;
const int N=1e5+10;
int n,a[N],b[N],id;
vector<int> e[N];
map<int,int> M;
bool vis[N];
void dfs(int x){
	vis[x]=1;
	for (int i=0;i<e[x].size();i++)
	if (!vis[e[x][i]]) dfs(e[x][i]);
}
int main()
{
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&a[i]),a[0]^=a[i];
	for (int i=1;i<=n;i++) scanf("%d",&b[i]),b[0]^=b[i];
	for (int i=0;i<=n;i++) M[a[i]]++,M[b[i]]--;
	for (int i=0;i<=n;i++)
		if (M[a[i]]) return puts("-1"),0;
	for (int i=0;i<=n;i++)
		if (!M[a[i]]) M[a[i]]=++id;
	int ans=0;
	for (int i=0;i<=n;i++)
		if (a[i]!=b[i]) e[M[a[i]]].push_back(M[b[i]]),ans++;
	for (int i=1;i<=id;i++)
		if (!vis[i]&&!e[i].empty()) dfs(i),ans++;
	if (!e[M[a[0]]].empty()) ans--;
	if (a[0]!=b[0]) ans--;
	printf("%d\n",ans);
	return 0;
}

```