#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <climits>
#include <stdlib.h>
#include <stdio.h>
using namespace std;
#define REP(i,n) for(int i=0; i<n; i++)
#define FOR(i,st,end) for(int i=st;i<end;i++)
#define db(x) cout << (#x) << " = " << x << endl;
#define mp make_pair
#define pb push_back
#define MAX 10000005
typedef long long int ll;
int main(){
	int n;
	int arr[100005];
	vector<int> ans;
	scanf("%d",&n);
	REP(i,n){
		scanf("%d",&arr[i]);

	}
	sort(arr,arr+n);
	if(n==1){
		cout<<"-1";
		return 0;
	}
	if(n==2){
		int diff=arr[1]-arr[0];
		if(diff==0){
				cout<<"1"<<endl<<arr[0];
				return 0;
			}
		if(diff!=0&&diff%2==0){
			ans.pb(arr[0]+diff/2);
		}
		ans.pb(arr[0]-diff);
		ans.pb(arr[1]+diff);
	}
	else{
		map<int,int> m;
		FOR(i,1,n){
			m[arr[i]-arr[i-1]]++;
		}
		int ms=m.size();
		map<int,int>::iterator it;
		if(ms==1){
			it=m.begin();
			if(it->first==0){
				cout<<"1"<<endl<<arr[0];
				return 0;
			}
			ans.pb(arr[0]-it->first);
			ans.pb(arr[n-1]+it->first);

		}
		else if(ms==2){
			vector<pair<int,int> >p;
			int minCountValue,maxCountValue;
			for(it=m.begin();it!=m.end();it++){
				p.pb(mp(it->first,it->second));
			}
			if(p[0].second==1||p[1].second==1){
				if(p[0].second==p[1].second){
					if(p[0].first<p[1].first){
						minCountValue=p[1].first;
						maxCountValue=p[0].first;
					}
				}
				else if(p[0].second<p[1].second){
					minCountValue=p[0].first;
					maxCountValue=p[1].first;
				}
				else{
					minCountValue=p[1].first;
					maxCountValue=p[0].first;
				}
				if(maxCountValue*2==minCountValue){
					FOR(i,1,n){
						if(arr[i]-arr[i-1]==minCountValue){
							ans.pb(arr[i-1]+maxCountValue);
						}
					}

				}
				else{
					cout<<"0";
					return 0;
				}
			}
			else{
				cout<<"0";
				return 0;
			}

		}
	}
	int ansSize=ans.size();
	cout<<ansSize<<endl;
	sort(ans.begin(),ans.end());
	REP(i,ansSize){
		cout<<ans[i]<<" ";
	}
}