#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
#include <map>
using namespace std;

const int MAXN = 2e5 + 10;
int N;
int A[MAXN], B[MAXN];
int fa[MAXN], tot;
map<int, int> mp;
int ans;

inline int gf(int x) {return x == fa[x] ? x : fa[x] = gf(fa[x]);}

int main() {
	register int i;
	scanf("%d", &N);
	for(i = 1; i <= N; ++i) scanf("%d", A + i), A[0] ^= A[i];
	for(i = 1; i <= N; ++i) scanf("%d", B + i), B[0] ^= B[i];
	for(i = 1; i <= N; ++i) fa[i] = i;
	for(i = 0; i <= N; ++i)
		if(A[i] != B[i] || i == 0) {
			++ans;
			if(!mp[A[i]]) mp[A[i]] = ++tot;
			if(!mp[B[i]]) mp[B[i]] = ++tot;
			fa[gf(mp[A[i]])] = gf(mp[B[i]]);
		}
	--ans;
	for(i = 1; i <= tot; ++i) if(fa[i] == i) ++ans;
	sort(A, A + N + 1); sort(B, B + N + 1);
	for(i = 0; i <= N; ++i) if(A[i] != B[i]) return puts("-1"), 0;
	printf("%d\n", ans - 1);
	return 0;
}
### 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 <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
#include <map>
using namespace std;

const int MAXN = 2e5 + 10;
int N;
int A[MAXN], B[MAXN];
int fa[MAXN], tot;
map<int, int> mp;
int ans;

inline int gf(int x) {return x == fa[x] ? x : fa[x] = gf(fa[x]);}

int main() {
	register int i;
	scanf("%d", &N);
	for(i = 1; i <= N; ++i) scanf("%d", A + i), A[0] ^= A[i];
	for(i = 1; i <= N; ++i) scanf("%d", B + i), B[0] ^= B[i];
	for(i = 1; i <= N; ++i) fa[i] = i;
	for(i = 0; i <= N; ++i)
		if(A[i] != B[i] || i == 0) {
			++ans;
			if(!mp[A[i]]) mp[A[i]] = ++tot;
			if(!mp[B[i]]) mp[B[i]] = ++tot;
			fa[gf(mp[A[i]])] = gf(mp[B[i]]);
		}
	--ans;
	for(i = 1; i <= tot; ++i) if(fa[i] == i) ++ans;
	sort(A, A + N + 1); sort(B, B + N + 1);
	for(i = 0; i <= N; ++i) if(A[i] != B[i]) return puts("-1"), 0;
	printf("%d\n", ans - 1);
	return 0;
}
```