#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define op(x) ((x&1)?x+1:x-1)
#define odd(x) (x&1)
#define even(x) (!odd(x))
#define lc(x) (x<<1)
#define rc(x) (lc(x)|1)
#define lowbit(x) (x&-x)
#define mp(x,y) make_pair(x,y)
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
using namespace std;
const int MAXN=5010;

int T,n,a[MAXN],mn;
ll S,ans;
ll s[MAXN];

void solve(){
	cin>>n;S=0;mn=1e9;
	rep(i,1,n)cin>>a[i],S+=a[i],mn = min(mn,a[i]);
	if(S<0 || (S==0 && mn < 0)){
		cout<<"-1\n";
		return;
	}
	if(S==0){
		cout<<"0\n";
		return;
	}

	ans=0;
	rep(i,1,n)s[i] = s[i-1] + a[i];
	rep(i,1,n)rep(j,i+1,n){
		ll px=(s[i] >= 0) ? -(s[i] / S) : ((-s[i] + S-1)/S);
		ll py=(s[j] >= 0) ? -(s[j] / S) : ((-s[j] + S-1)/S);

		ll vx = (s[i] % S + S)%S,vy = (s[j] % S + S)%S;

		if(vx == vy)ans += abs(px-py) - (px>py);
		else if(vx < vy)ans += abs(px-py);
		else ans += abs(px-py) + ((px <= py) ? (1) : (-1));
	}
	cout<<ans<<"\n";
}

int main(){

	ios::sync_with_stdio(false);
	cin>>T;
	while(T--)solve();

    return 0;
}