#include<bits/stdc++.h>
using namespace std;
#define int long long
int n,m,a[300010],sum[300010],tree[300010],b[300010];
void add(int x,int y){for(;x<=m;x+=x&-x) tree[x]+=y;}
int query(int x){
	int res=0;
	for(;x;x&=x-1) res+=tree[x];
	return res;
}
signed main(){
	while(cin>>n&&n){
    	for(int i=1;i<=n;i++) cin>>a[i],sum[i]=sum[i-1]+a[i];
    	int z=sum[n],ans=0;
    	if(z<0){cout<<"-1\n";continue;}
    	if(!z){
    		int f=0;
		    for(int i=1;i<=n;i++){
		    	if(a[i]){
			    	cout<<"-1\n";
			    	f=1;break;
		    	}
		    }
	    	if(!f) cout<<"0\n";
			continue;
    	}
    	for(int i=1;i<=n;i++){
		    b[++m]=sum[i];
			b[++m]=(sum[i]%z+z)%z;
		}
	    sort(b+1,b+m+1);
		m=unique(b+1,b+m+1)-b-1;
	    memset(tree,0,sizeof(tree));
    	for(int i=1;i<=n;i++){
		    ans-=query(lower_bound(b+1,b+m+1,sum[i])-b-1);
		    add(lower_bound(b+1,b+m+1,sum[i])-b,1);
	    }
	    sort(sum+1,sum+n+1);
	    memset(tree,0,sizeof(tree));
	    for(int i=1;i<=n;i++){
		    ans+=(i*2-1ll-n)*(sum[i]>0?sum[i]/z:(sum[i]-z+1)/z)+query(lower_bound(b+1,b+m+1,(sum[i]%z+z)%z)-b-1);
		    add(lower_bound(b+1,b+m+1,(sum[i]%z+z)%z)-b,1);
    	}
    	cout<<ans<<"\n";
    	memset(sum,0,sizeof(sum));
        memset(b,0,sizeof(b));
        memset(a,0,sizeof(a));
        memset(tree,0,sizeof(tree));
    	m=0;
	}
	return 0;
}