#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <map>
#define MAXN 200010
std::map<int, int> M;
int a[MAXN], b[MAXN], c[MAXN], d[MAXN], p[MAXN], n, m;
inline int find(int x) { return x == p[x] ? x : p[x] = find(p[x]); }
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];
	memcpy(c, a, sizeof(c));
	memcpy(d, b, sizeof(d));
	std::sort(c, c + n + 1);
	std::sort(d, d + n + 1);
	for (int i = 0; i <= n; i++)
		if (c[i] != d[i]) return puts("-1"), 0;
	for (int i = 0; i <= n; i++)
		if (a[i] != b[i]) goto fail;
	return puts("0"), 0;
fail:
	int ans = 0;
	for (int i = 0; i <= n; i++) {
		if (!i || a[i] != b[i]) {
			if (!M.count(a[i])) {
				M[a[i]] = ++m;
				p[m] = m;
			}
			if (!M.count(b[i])) {
				M[b[i]] = ++m;
				p[m] = m;
			}
			int A = find(M[a[i]]), B = find(M[b[i]]);
			if (A != B) p[A] = B;
			ans += i > 0;
		}
	}
	for (int i = 1; i <= m; i++)
		if (find(i) == i) ans++;
	printf("%d\n", ans - 1);
	return 0;
}
### Prompt

Create a solution in Cpp for 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 <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <map>
#define MAXN 200010
std::map<int, int> M;
int a[MAXN], b[MAXN], c[MAXN], d[MAXN], p[MAXN], n, m;
inline int find(int x) { return x == p[x] ? x : p[x] = find(p[x]); }
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];
	memcpy(c, a, sizeof(c));
	memcpy(d, b, sizeof(d));
	std::sort(c, c + n + 1);
	std::sort(d, d + n + 1);
	for (int i = 0; i <= n; i++)
		if (c[i] != d[i]) return puts("-1"), 0;
	for (int i = 0; i <= n; i++)
		if (a[i] != b[i]) goto fail;
	return puts("0"), 0;
fail:
	int ans = 0;
	for (int i = 0; i <= n; i++) {
		if (!i || a[i] != b[i]) {
			if (!M.count(a[i])) {
				M[a[i]] = ++m;
				p[m] = m;
			}
			if (!M.count(b[i])) {
				M[b[i]] = ++m;
				p[m] = m;
			}
			int A = find(M[a[i]]), B = find(M[b[i]]);
			if (A != B) p[A] = B;
			ans += i > 0;
		}
	}
	for (int i = 1; i <= m; i++)
		if (find(i) == i) ans++;
	printf("%d\n", ans - 1);
	return 0;
}
```