#include<bits/stdc++.h>
#define inf 1e9
#define eps 1e-6
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define REP(i,a,b) for(int i=a;i>=b;i--)
#define mp make_pair
#define pa pair<int,int>
#define fr first
#define sd second
#define pb push_back
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define int ll
inline ll read()
{
	char ch=getchar();
	ll s=0,w=1;
	while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){s=s*10+ch-'0';ch=getchar();}
	return s*w;
}
#define N 1000010
struct node
{
	int a,b;
};
inline bool operator <(const node &x,const node &y)
{
	int v=x.b/gcd(x.b,y.b)*y.b;
	return x.a*v/x.b<y.a*v/y.b;
}
int T,n,a[N],s[N];
int gcd(int x,int y){return (!y?x:gcd(y,x%y));}
inline void sol()
{
	n=read();
	FOR(i,1,n)a[i]=read();
	vector<int>G;int S=1,flag=0,v=1;s[0]=1;
	FOR(i,1,n)
	{
		if(a[i]==0)G.pb(i);
		if(a[i]>=0)S++,v++,s[i]=s[i-1]+1;
		else S--,s[i]=s[i-1]-1;
		if(S<=0)flag=1;
	}
	if(flag){cout<<"-1\n";return ;}
	node ans;ans.a=v,ans.b=S;
	// cout<<"GG:"<<ans.a<<" "<<ans.b<<endl;
	int w=inf;
	REP(i,n,1)
	{
		w=min(w,s[i]);
		// cout<<i<<" "<<a[i]<<" "<<w<<endl;
		if(w<=2)break;
		if(a[i]==0)
		{
			v--,S-=2;w-=2;
			node tmp;tmp.a=v,tmp.b=S;
			// cout<<"EE:"<<tmp.a<<" "<<tmp.b<<endl;
			if(ans<tmp)ans=tmp;
		}
	}
	int t=gcd(ans.a,ans.b);
	cout<<ans.a/t<<' '<<ans.b/t<<'\n';
}
signed main()
{
	T=read();while(T--)sol();
	return 0;
}