#include<bits/stdc++.h>
using namespace std;
const int N = 1e5+10;
int n,b[N],d[N],tot,sum;
int main(){
	cin>>n;
	for(int i=1;i<=n;i++){cin>>b[i];}
	if(n<=2){cout<<0;return 0;}
	for(int i=2;i<=n;i++){d[i-1]=b[i]-b[i-1];sum+=d[i-1];d[i-1]=abs(d[i-1]);}
	sum=abs(sum);
	sum=sum%(n-1)==0? sum/(n-1):sum/(n-1)+1;
	for(int i=1;i<n-1;i++) if(d[i]==d[i+1]) tot++;
	if(tot==n-2) cout<<0;//如果已经是等差数列，就输出
	else{
	    int ans=0;
	    for(int i=1;i<n-1;i++){
	    	if(d[i]<sum){ans++;d[i]++;continue;}
			if(d[i]==sum) continue;
			if(d[i]>sum){
		        if(d[i-1]<sum){d[i-1]++;d[i]--;ans++;}
		        if(d[i]==sum) continue;
				if(d[i+1]<sum){d[i+1]++;d[i]--;ans++;}
				if(d[i]>sum){d[i]--;ans++;}
				continue;
			} 
		}
		if(d[n-1]>sum&&d[n-2]<sum){d[n-1]--;d[n-2]++;ans++;}
		if(d[n-1]>sum){d[n-1]--;ans++;}
		int tot=0;
		for(int i=1;i<n-1;i++){if(d[i]==d[i+1]) tot++;} 
		if(tot==n-2) cout<<ans;
		else cout<<-1;
	}
	return 0;
}