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

const int N = 2e5 + 9;

unordered_map<int, int>T, W;
int a[N], b[N], n, h[N], t, f[N], ret;

int find (int x) { return x == f[x] ? x : f[x] = find(f[x]); }

int main () {
	scanf("%d", &n);
	for (int i = 0; i < n; ++i) scanf("%d", &a[i]), a[n] ^= a[i];
	for (int i = 0; i < n; ++i) scanf("%d", &b[i]), b[n] ^= b[i];
	for (int i = 0; i <= n; ++i) ++T[a[i]], --T[b[i]];
	for (auto u : T) if (u.second) return puts("-1"), 0;
	for (int i = 0; i <= n; ++i) if (i == n || a[i] != b[i]) h[t++] = a[i], h[t++] = b[i];
	sort(h, h + t);
	t = unique(h, h + t) - h;
	for (int i = 0; i <= n; ++i) if (i == n || a[i] != b[i]) {
		a[i] = lower_bound(h, h + t, a[i]) - h, b[i] = lower_bound(h, h + t, b[i]) - h;
		if (i < n) ++ret;
	}
	for (int i = 0; i < t; ++i) f[i] = i;
	for (int i = 0; i <= n; ++i) if (a[i] != b[i]) f[find(a[i])] = find(b[i]);
	for (int i = 0; i < t; ++i) if (find(i) == i) ++ret;
	printf("%d\n", ret - (bool)t);
	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<bits/stdc++.h>
using namespace std;

const int N = 2e5 + 9;

unordered_map<int, int>T, W;
int a[N], b[N], n, h[N], t, f[N], ret;

int find (int x) { return x == f[x] ? x : f[x] = find(f[x]); }

int main () {
	scanf("%d", &n);
	for (int i = 0; i < n; ++i) scanf("%d", &a[i]), a[n] ^= a[i];
	for (int i = 0; i < n; ++i) scanf("%d", &b[i]), b[n] ^= b[i];
	for (int i = 0; i <= n; ++i) ++T[a[i]], --T[b[i]];
	for (auto u : T) if (u.second) return puts("-1"), 0;
	for (int i = 0; i <= n; ++i) if (i == n || a[i] != b[i]) h[t++] = a[i], h[t++] = b[i];
	sort(h, h + t);
	t = unique(h, h + t) - h;
	for (int i = 0; i <= n; ++i) if (i == n || a[i] != b[i]) {
		a[i] = lower_bound(h, h + t, a[i]) - h, b[i] = lower_bound(h, h + t, b[i]) - h;
		if (i < n) ++ret;
	}
	for (int i = 0; i < t; ++i) f[i] = i;
	for (int i = 0; i <= n; ++i) if (a[i] != b[i]) f[find(a[i])] = find(b[i]);
	for (int i = 0; i < t; ++i) if (find(i) == i) ++ret;
	printf("%d\n", ret - (bool)t);
	return 0;
}
```