#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define f(i, x, n) for(int i = x; i < (int)(n); ++i)

int A[100001], B[100000];
map<int, int> fra;
map<int, vector<int> > b;
bool vis[100001], g[100001];
set<int> vis2;

int go(int v){
	if (vis[v])return 0;
	vis[v] = true;
	int an = 1;
	if (vis2.find(A[v]) != vis2.end())return an;
	vis2.insert(A[v]);
	vector<int> &vc = b[A[v]];
	f(i, 0, vc.size())an += go(vc[i]);
	return an;
}

int main(){
	int n;
	scanf("%d", &n);
	int x = 0;
	f(i, 0, n)scanf("%d", A + i), x ^= A[i], ++fra[A[i]];
	A[n] = x;
	int ok = 0, x2 = 0;
	f(i, 0, n){
		scanf("%d", B + i);
		x2 ^= B[i];
		if (B[i] == A[i])++ok, --fra[A[i]], g[i] = true;
		else b[B[i]].push_back(i);
	}
	b[x2].push_back(n);
	++fra[x];
	for (map<int, vector<int> >::iterator it = b.begin(); it != b.end(); ++it)if (fra[it->first] != (int)it->second.size()) { printf("-1\n"); return 0; }
	int an = go(n) - 1;
	f(i, 0, n)if (!g[i] && !vis[i])an += go(i) + 1;
	printf("%d\n", an);
}
### Prompt

Generate 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 <bits/stdc++.h>
using namespace std;
#define ll long long
#define f(i, x, n) for(int i = x; i < (int)(n); ++i)

int A[100001], B[100000];
map<int, int> fra;
map<int, vector<int> > b;
bool vis[100001], g[100001];
set<int> vis2;

int go(int v){
	if (vis[v])return 0;
	vis[v] = true;
	int an = 1;
	if (vis2.find(A[v]) != vis2.end())return an;
	vis2.insert(A[v]);
	vector<int> &vc = b[A[v]];
	f(i, 0, vc.size())an += go(vc[i]);
	return an;
}

int main(){
	int n;
	scanf("%d", &n);
	int x = 0;
	f(i, 0, n)scanf("%d", A + i), x ^= A[i], ++fra[A[i]];
	A[n] = x;
	int ok = 0, x2 = 0;
	f(i, 0, n){
		scanf("%d", B + i);
		x2 ^= B[i];
		if (B[i] == A[i])++ok, --fra[A[i]], g[i] = true;
		else b[B[i]].push_back(i);
	}
	b[x2].push_back(n);
	++fra[x];
	for (map<int, vector<int> >::iterator it = b.begin(); it != b.end(); ++it)if (fra[it->first] != (int)it->second.size()) { printf("-1\n"); return 0; }
	int an = go(n) - 1;
	f(i, 0, n)if (!g[i] && !vis[i])an += go(i) + 1;
	printf("%d\n", an);
}
```