#include <bits/stdc++.h>
using namespace std;
#define ll int
#define N ((ll)101*1000)

ll n,k,a[N],b[N],ans,v[N],cnt_v;
map <ll,ll> mp;
vector <ll> e[N];
bool mark[N];

ll _find(ll x){return lower_bound(v,v+cnt_v,x)-v;}

void dfs(ll x)
{
	mark[x]=1;
	for(auto u:e[x])
		if(!mark[u])
			dfs(u);
}

int main()
{
	ios_base::sync_with_stdio(0);cin.tie(0);
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i],a[0]^=a[i],mp[a[i]]++,v[cnt_v++]=a[i];
	mp[a[0]]++;
	v[cnt_v++]=a[0];
	sort(v,v+cnt_v);cnt_v=unique(v,v+cnt_v)-v;
	for(int i=1;i<=n;i++)
	{
		cin>>b[i];
		mp[b[i]]--;
		if(mp[b[i]]<0)return cout<<"-1\n",0;
		if(b[i]!=a[i])e[_find(a[i])].push_back(_find(b[i])),ans++;
	}
	for(auto u:mp)
		if(u.second)
			e[_find(a[0])].push_back(_find(u.first)),ans++;
	ans-=2;
	for(int i=0;i<cnt_v;i++)
		if(!mark[i])
		{
			dfs(i);
			if(e[i].size())ans++;
		}
	cout<<ans<<"\n";
	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;
#define ll int
#define N ((ll)101*1000)

ll n,k,a[N],b[N],ans,v[N],cnt_v;
map <ll,ll> mp;
vector <ll> e[N];
bool mark[N];

ll _find(ll x){return lower_bound(v,v+cnt_v,x)-v;}

void dfs(ll x)
{
	mark[x]=1;
	for(auto u:e[x])
		if(!mark[u])
			dfs(u);
}

int main()
{
	ios_base::sync_with_stdio(0);cin.tie(0);
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i],a[0]^=a[i],mp[a[i]]++,v[cnt_v++]=a[i];
	mp[a[0]]++;
	v[cnt_v++]=a[0];
	sort(v,v+cnt_v);cnt_v=unique(v,v+cnt_v)-v;
	for(int i=1;i<=n;i++)
	{
		cin>>b[i];
		mp[b[i]]--;
		if(mp[b[i]]<0)return cout<<"-1\n",0;
		if(b[i]!=a[i])e[_find(a[i])].push_back(_find(b[i])),ans++;
	}
	for(auto u:mp)
		if(u.second)
			e[_find(a[0])].push_back(_find(u.first)),ans++;
	ans-=2;
	for(int i=0;i<cnt_v;i++)
		if(!mark[i])
		{
			dfs(i);
			if(e[i].size())ans++;
		}
	cout<<ans<<"\n";
	return 0;
}
```