#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,b) for(ll i=a;i<b;i++)
#define rrep(i,a,b) for(ll i=a-1;i>=b;i--)
#define ll long long
#define ull unsigned ll
#define ld long double
#define bl __int128_t
#define fi first
#define se second
#define vel vector<ll>
#define vvel vector<vel>
#define pll pair<ll,ll>
#define vepll vector<pll>
#define vvepll vector<vepll>
#define ves vector<string>
#define vem vector<mint>
#define vvem vector<vem>
#define pmm pair<mint,mint>
#define cleout(i) cout<<fixed<<setprecision(i)
template<class T>using PQ=priority_queue<T,vector<T>,greater<T>>;
//               上  右 下 左
vector<int> di={-1, 0, 1, 0};
vector<int> dj={ 0, 1, 0,-1};

vector<int> dx={ 0, 1, 0,-1};
vector<int> dy={ 1, 0,-1, 0};


vector<int> ddx={ 1, 1, 1, 0, -1, -1, -1, 0 };
vector<int> ddy={ 1, 0, -1, -1, -1, 0, 1, 1 };

ll inf=1000000000000000000;//1e18
// LLONG_MAX

mt19937_64 rng((ull)chrono::steady_clock::now().time_since_epoch().count());



void _solve(){
    ll N;
    cin>>N;
    vel a(N);
    rep(i,0,N){
        cin>>a[i];
    }
    auto f=[&](ll mid){
        vel sum(mid+1,0);
        rep(i,0,a.size()){
            if(a[i]>=mid)sum[0]++;
            else sum[a[i]]++;
        }
        sum[0]+=sum[1];
        sum[1]=0;
        ll now=1;
        rrep(i,mid,1){
            if(sum[i]>=now){
                sum[i]-=now;
            }else{
                now+=(now-sum[i]);
            }
            if(sum[i]){
                sum[0]+=sum[i];
            }
            if(now>N)return 0ll;
        }
        return (ll)(now<=sum[0]);
    };
    ll ok=1;
    ll ng=a.size()+1;
    while(ng-ok>1){
        ll mid=(ok+ng)/2;
        if(f(mid))ok=mid;
        else ng=mid;
    }
    cout<<ok<<"\n";
}


int main(){
    cin.tie(nullptr);
 	ios_base::sync_with_stdio(false);
    
    ll _;
    bool multitest=1;
    if(multitest)cin>>_;
    else _=1;
    rep(__,0,_){
        _solve();
    }
}