#include<bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define pb push_back
using namespace std;
using ll = long long;
using vi = vector<ll>;
using pi = pair<ll, ll>;
const int maxn = 1e5 + 55;//, mod = 1e9 + 7;
int n, e, c, sz = 0;
int a[maxn], b[maxn], vis[maxn];
map<int, int> id, cnt;
vi g[maxn];
int getid(int x) {
	if(!id.count(x)) id[x] = sz++;
	return id[x];
}
void add_edge(int u, int v) {
	e++;
	g[u].pb(v);
	g[v].pb(u);
}
void dfs(int v) {
	vis[v] = 1;
	for(int i : g[v])
		if(!vis[i]) dfs(i);
}
void solve() {
	for(int i = 0; i < sz; i++) if(!vis[i]) c++, dfs(i);
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for(int i = 1; i <= n; i++) cin >> a[i], a[0] ^= a[i], cnt[a[i]]++;
	for(int i = 1; i <= n; i++) cin >> b[i], b[0] ^= b[i], cnt[b[i]]--;
	cnt[a[0]]++, cnt[b[0]]--;
	for(auto i : cnt) if(i.second) return cout << -1, 0;
	for(int i = 1; i <= n; i++) {
		if(a[i]!=b[i]) add_edge(getid(a[i]), getid(b[i]));
	}
	int zero = 1;
	for(int i = 0; i < n; i++) zero &= a[i] == b[i];
	if(zero) return cout << 0, 0;
	getid(a[0]);
	getid(b[0]);
	solve();
	cout << e + c - 1;
}

### 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>
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define pb push_back
using namespace std;
using ll = long long;
using vi = vector<ll>;
using pi = pair<ll, ll>;
const int maxn = 1e5 + 55;//, mod = 1e9 + 7;
int n, e, c, sz = 0;
int a[maxn], b[maxn], vis[maxn];
map<int, int> id, cnt;
vi g[maxn];
int getid(int x) {
	if(!id.count(x)) id[x] = sz++;
	return id[x];
}
void add_edge(int u, int v) {
	e++;
	g[u].pb(v);
	g[v].pb(u);
}
void dfs(int v) {
	vis[v] = 1;
	for(int i : g[v])
		if(!vis[i]) dfs(i);
}
void solve() {
	for(int i = 0; i < sz; i++) if(!vis[i]) c++, dfs(i);
}
int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for(int i = 1; i <= n; i++) cin >> a[i], a[0] ^= a[i], cnt[a[i]]++;
	for(int i = 1; i <= n; i++) cin >> b[i], b[0] ^= b[i], cnt[b[i]]--;
	cnt[a[0]]++, cnt[b[0]]--;
	for(auto i : cnt) if(i.second) return cout << -1, 0;
	for(int i = 1; i <= n; i++) {
		if(a[i]!=b[i]) add_edge(getid(a[i]), getid(b[i]));
	}
	int zero = 1;
	for(int i = 0; i < n; i++) zero &= a[i] == b[i];
	if(zero) return cout << 0, 0;
	getid(a[0]);
	getid(b[0]);
	solve();
	cout << e + c - 1;
}

```