#include<cstdio>
#include<algorithm>
#include<map>
using namespace std;
#define MAXN 200010
int Adj[MAXN],V[MAXN],nxt[MAXN],c;
void AddEdge(int u,int v)
{
	c++;V[c]=v,nxt[c]=Adj[u];Adj[u]=c;
}
int a[MAXN],b[MAXN],n,cnt,in[MAXN],out[MAXN],x,ans,pcnt;
map<int,int>G;
int vis[MAXN];
void dfs(int u)
{
	vis[u]=1;
	for(int i=Adj[u];i;i=nxt[i])
		if(!vis[V[i]])
			dfs(V[i]);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		x^=a[i];
		if(G[a[i]]==0) G[a[i]]=++cnt;
		a[i]=G[a[i]];
	}
	if(G[x]==0) G[x]=++cnt;
	x=G[x];
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&b[i]);
		if(G[b[i]]==0) G[b[i]]=++cnt;
		b[i]=G[b[i]];
	}
	for(int i=1;i<=n;i++)
	{
		if(a[i]==b[i]) continue;
		AddEdge(b[i],a[i]);
		in[a[i]]++,out[b[i]]++;
		ans++;
	}
	for(int i=1;i<=cnt;i++)
		if(in[i]!=out[i])
		{
			if(in[i]<out[i])
			{
				if(out[i]!=in[i]+1||i!=x)
				{
					printf("-1\n");
					return 0;
				}
			}
			else
			{
				if(in[i]!=out[i]+1||pcnt)
				{
					printf("-1\n");
					return 0;
				}
				pcnt++;
			}
		}
	dfs(x);
	for(int i=1;i<=cnt;i++)
		if(out[i]&&!vis[i])
		{
			dfs(i);
			ans++;
		}
	printf("%d\n",ans);
}
### 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<cstdio>
#include<algorithm>
#include<map>
using namespace std;
#define MAXN 200010
int Adj[MAXN],V[MAXN],nxt[MAXN],c;
void AddEdge(int u,int v)
{
	c++;V[c]=v,nxt[c]=Adj[u];Adj[u]=c;
}
int a[MAXN],b[MAXN],n,cnt,in[MAXN],out[MAXN],x,ans,pcnt;
map<int,int>G;
int vis[MAXN];
void dfs(int u)
{
	vis[u]=1;
	for(int i=Adj[u];i;i=nxt[i])
		if(!vis[V[i]])
			dfs(V[i]);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		x^=a[i];
		if(G[a[i]]==0) G[a[i]]=++cnt;
		a[i]=G[a[i]];
	}
	if(G[x]==0) G[x]=++cnt;
	x=G[x];
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&b[i]);
		if(G[b[i]]==0) G[b[i]]=++cnt;
		b[i]=G[b[i]];
	}
	for(int i=1;i<=n;i++)
	{
		if(a[i]==b[i]) continue;
		AddEdge(b[i],a[i]);
		in[a[i]]++,out[b[i]]++;
		ans++;
	}
	for(int i=1;i<=cnt;i++)
		if(in[i]!=out[i])
		{
			if(in[i]<out[i])
			{
				if(out[i]!=in[i]+1||i!=x)
				{
					printf("-1\n");
					return 0;
				}
			}
			else
			{
				if(in[i]!=out[i]+1||pcnt)
				{
					printf("-1\n");
					return 0;
				}
				pcnt++;
			}
		}
	dfs(x);
	for(int i=1;i<=cnt;i++)
		if(out[i]&&!vis[i])
		{
			dfs(i);
			ans++;
		}
	printf("%d\n",ans);
}
```