#include <bits/stdc++.h>

using namespace std;

const int MAXN = 100010;

map<int, int>mp;
map<int, int>fa;

int a[MAXN];
int b[MAXN];

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

inline int Merge(int x, int y) {
    int fx = find(x), fy = find(y);
    if(fx == fy) return 0;
    fa[fx] = fy;
    return 1;
}

int main() {
    ios::sync_with_stdio(false);
    int n, Xor = 0, flag = 0;
    cin >> n;
    for(int i = 1; i <= n; i++) cin >> a[i], mp[a[i]]++, Xor ^= a[i];
    a[n + 1] = Xor, mp[Xor]++;
    for(int i = 1; i <= n; i++) {
        int &x = b[i];
        cin >> x;
        if(!mp[x]) return puts("-1"), 0;
        mp[x]--;
    }
    for(int i = 1; i <= n; i++) {
        if(a[i] != b[i]) {
            fa[a[i]] = a[i];
            fa[b[i]] = b[i];
        }
    } fa[Xor] = Xor;
    int res = fa.size();
    for(int i = 1; i <= n; i++) {
        if(a[i] != b[i])
            res -= Merge(a[i], b[i]), ++res;
    } res--;
    cout << res << endl;
    return 0;
}
### Prompt

Your challenge is to write 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;

const int MAXN = 100010;

map<int, int>mp;
map<int, int>fa;

int a[MAXN];
int b[MAXN];

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

inline int Merge(int x, int y) {
    int fx = find(x), fy = find(y);
    if(fx == fy) return 0;
    fa[fx] = fy;
    return 1;
}

int main() {
    ios::sync_with_stdio(false);
    int n, Xor = 0, flag = 0;
    cin >> n;
    for(int i = 1; i <= n; i++) cin >> a[i], mp[a[i]]++, Xor ^= a[i];
    a[n + 1] = Xor, mp[Xor]++;
    for(int i = 1; i <= n; i++) {
        int &x = b[i];
        cin >> x;
        if(!mp[x]) return puts("-1"), 0;
        mp[x]--;
    }
    for(int i = 1; i <= n; i++) {
        if(a[i] != b[i]) {
            fa[a[i]] = a[i];
            fa[b[i]] = b[i];
        }
    } fa[Xor] = Xor;
    int res = fa.size();
    for(int i = 1; i <= n; i++) {
        if(a[i] != b[i])
            res -= Merge(a[i], b[i]), ++res;
    } res--;
    cout << res << endl;
    return 0;
}
```