#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll>pi;
#define int ll
#define X first
#define Y second
#define fer(i,a,n) for(int i=a;i<=n;i++)
#define ref(i,n,a) for(int i=n;i>=a;i--)
#define endl '\n'
#define mem(a,x) memset(a,x,sizeof a)
#define ac IO;int t;cin>>t;while(t--)solve()
#define AC signed main(){IO;solve();}
#define NO {cout<<"No"<<endl;return;}
#define YES {cout<<"Yes"<<endl;return;}
#define re(a) {cout<<a<<endl;return;}
#define V vector<int>
#define all(v) v.begin(),v.end()
//ofstream fout("out.txt", ios::out);
//ifstream fin("in.txt", ios::in);
//#define cout fout
//#define cin fin
//--------------------瑞神神中神--------------------
//--------------------刘魔魔中魔--------------------

const int N=1e6+10;
int a[N],f[N],g[N];
int n;

void solve()
{
    cin>>n;
    fer(i,1,n)
    {
        cin>>a[i];
    }
    f[n+1]=g[n+1]=0;
    for(int i=n;i>=1;i--)
    {
        int w=a[i];
        if(!w)w++;
        g[i]=max(g[i+1],0ll)-w;
        f[i]=max(f[i+1],g[i]);
    }
    int sum=1,cnt=1;
    for(int i=1;i<=n;i++)
    {
        if(a[i]==1)
        {
            sum++;cnt++;
        }
        else if(a[i]==-1)
        {
            if(cnt<=1)re(-1);
            cnt--;
        }
        else
        {
            if(cnt-1-f[i+1]>=1)
            {
                cnt--;
            }
            else
            {
                sum++;cnt++;
            }
        }
    }
    int gd=gcd(sum,cnt);
    cout<<sum/gd<<' '<<cnt/gd<<endl;
}

signed main()
{
    ac;
}