#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define MP make_pair
mt19937 rnd(time(0));
const int MAXN=1e6+5;
int n,a[MAXN],b[MAXN];
bool check(int x){
//	cout<<"Check "<<x<<endl;
	for(int i=n;i>=1;i--){
		if(a[i]!=0) b[i]=a[i];
		else b[i]=(x-->0?-1:1);
	}
//	for(int i=1;i<=n;i++) cout<<b[i]<<' ';cout<<endl;
	int q=1;
	for(int i=1;i<=n;i++){
		if(b[i]==1) q++;
		else q--;
		if(q==0) return false;
	}
	return true;
}
void solve(){
	cin>>n;
	int l=0,r=0,s=0,mid;
	for(int i=1;i<=n;i++) cin>>a[i],s+=(a[i]==0);
	r=s;
	if(!check(0)){cout<<"-1"<<endl;return;}
	while(l<r){
		mid=l+r+1>>1;
		if(check(mid)) l=mid;
		else r=mid-1;
	} 
	int p=1,q=1;
	for(int i=1;i<=n;i++){
		if(a[i]==1) p++,q++;
		else if(a[i]==-1) q--;
	}
	ll ap=0,aq=1;
	for(int i=0;i<=l;i++){
		ll np=p+(s-i),nq=q+(s-i)-i;
		if(ap*nq<np*aq) ap=np,aq=nq;
	}
	ll g=__gcd(ap,aq);
	cout<<ap/g<<' '<<aq/g<<endl;
}
int main(){
	ios::sync_with_stdio(false);
	int _;cin>>_;
	while(_--) solve();
}