// Templates and Snippets -> https://github.com/igeeeeee/template
#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#endif
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using i128 = __int128_t;
using u128 = __uint128_t;
ostream& operator<<(ostream& os, u128 x) {if (x >= 10) os << x / 10;return os << char('0' + x % 10);}
ostream& operator<<(ostream& os, i128 x){if (x < 0){os << '-';return os << (-(u128)x);}return os << (u128)x;}
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rrep(i,start,end) for (ll i = start;i >= (ll)(end);i--)
#define repn(i,end) for(ll i = 0; i <= (ll)(end); i++)
#define reps(i,start,end) for(ll i = start; i < (ll)(end); i++)
#define repsn(i,start,end) for(ll i = start; i <= (ll)(end); i++)
#define each(p,a) for(auto &p:a)
typedef vector<ll> vll;
typedef vector<pair<ll ,ll>> vpll;
typedef vector<vector<pair<ll ,ll>>> vvpll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef pair<ll ,ll> pll;
typedef pair<ull,ull> pull;
typedef tuple<ll , ll , ll> tpl3;
typedef tuple<ll , ll , ll , ll> tpl4;
typedef tuple<ll , ll , ll , ll , ll> tpl5;
typedef tuple<ll , ll , ll , ll , ll , ll> tpl6;
#define FI first
#define SE second
#define LL(...) ll __VA_ARGS__; input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; input(__VA_ARGS__)
#define Str(...) string __VA_ARGS__; input(__VA_ARGS__)
#define Ch(...) char __VA_ARGS__; input(__VA_ARGS__)
#define all(a)  (a).begin(),(a).end()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define sz(x) (ll)x.size()
// << std::fixed << std::setprecision(10)
const ll INF = 1LL << 60;
const ld EPS = 1e-9;
 
ll lceil(ll a,ll b){if(a%b==0){return a/b;}if(a>=0){return (a/b)+1;}else{return -((-a)/b);}}
ll lfloor(ll a,ll b){if(a%b==0){return a/b;}if(a>=0){return (a/b);}else{return -((-a)/b)-1;}}
inline ll positive_mod(ll a,ll m){return (a % m + m)%m;}
inline ll popcnt(ull a){ return __builtin_popcountll(a);}
//0indexed
inline ll topbit(ll a){assert(a != 0);return 63 - __builtin_clzll(a);}
inline ll smlbit(ll a){assert(a != 0);return __builtin_ctzll(a);}
template<class T> bool chmin(T& a, T b){if(a > b){a = b;return true;}return false;}
template<class T> bool chmax(T& a, T b){if(a < b){a = b;return true;}return false;}
template<typename T> std::istream &operator>>(std::istream&is,std::vector<T>&v){for(T &in:v){is>>in;}return is;}
template<typename T> std::ostream &operator<<(std::ostream&os,const std::vector<T>&v){for(auto it=std::begin(v);it!=std::end(v);){os<<*it<<((++it)!=std::end(v)?" ":"");}return os;}
template<typename T1, typename T2>std::ostream &operator<< (std::ostream &os, std::pair<T1,T2> p){os << "{" << p.first << "," << p.second << "}";return os;}
template<class... T>void input(T&... a){(cin >> ... >> a);}
void print(){cout << endl;}
template<class T, class... Ts>void print(const T& a, const Ts&... b){cout << a;((cout << ' ' << b), ...);cout << endl;}
template<class T> void pspace(const T& a){ cout << a << ' ';}
void perr(){cerr << endl;}
template<class T, class... Ts>void perr(const T& a, const Ts&... b){cerr << a;((cerr << ' ' << b), ...);cerr << endl;}
void yes(bool i = true){ return print(i?"yes":"no"); }
void Yes(bool i = true){ return print(i?"Yes":"No"); }
void YES(bool i = true){ return print(i?"YES":"NO"); }
template <class T> vector<T> &operator++(vector<T> &v) {for(auto &e : v) e++;return v;}
template <class T> vector<T> operator++(vector<T> &v, signed) {auto res = v;for(auto &e : v) e++;return res;}
template <class T> vector<T> &operator--(vector<T> &v) {for(auto &e : v) e--;return v;}
template <class T> vector<T> operator--(vector<T> &v, signed) {auto res = v;for(auto &e : v) e--;return res;}
//grid探索用
vector<ll> _ta = {0,0,1,-1,1,1,-1,-1};
vector<ll> _yo = {1,-1,0,0,1,-1,1,-1};
bool isin(ll now_i,ll now_j,ll h,ll w){return (0<=now_i && now_i < h && 0 <= now_j && now_j < w);}
  
ll lpow(ll x,ll n){ll ans = 1;while(n >0){if(n & 1)ans *= x;x *= x;n >>= 1;}return ans;}
ll Modlpow(ll x,ll n,ll m){ll ans = 1;ll a = x%m;while(n >0){if(n & 1){ans *= a;ans%= m;}a *= a;a %= m;n >>= 1;}return ans;} 
const ll MOD9 = 998244353LL;
const ll MOD10 = 1000000007LL;

void solve();
#ifdef DEBUG
void naive();
string run(void (*f)(), const string& input) {istringstream iss(input);ostringstream oss;auto* cinbuf = cin.rdbuf(iss.rdbuf());auto* coutbuf = cout.rdbuf(oss.rdbuf());cin.clear();f();cout.flush();cin.rdbuf(cinbuf);cout.rdbuf(coutbuf);cin.clear();return oss.str();}

bool check(const string& input) {
  string ans = run(solve, input);istringstream acin(ans);
  string correct = run(naive, input);istringstream ccin(correct);
  // ll x;acin >> x;とかで使える(構築とかの確認用)

  if (ans == correct) return true;//末尾の空白まで完全一致

  cerr << "========== INPUT ==========\n";
  cerr << input;
  cerr << "========== EXPECTED =======\n";
  cerr << correct;
  cerr << "========== ACTUAL =========\n";
  cerr << ans;
  cerr << "===========================\n";
  return false;
}

uint64_t seed = chrono::steady_clock::now().time_since_epoch().count();
mt19937_64 rng(seed);
ll rnd(ll l, ll r){// l 以上 r 以下
  return uniform_int_distribution<ll>(l, r)(rng);
}

void test(){
  rep(tc,100000){
    // ----- テストケース生成(文字列で!!) -----
    string input;
    ll n = rnd(1,10);
    input += to_string(n);
    input += '\n';

    // ----- 比較 -----
    check(input);

    if ((tc+1) % 1000 == 0) {
      cerr << tc+1 << " cases passed\n";
    }
  }
}

void naive(){//cinで受け取りcoutで出力でよい

}
#endif

//双対セグ木
//fm(f,g)はgにfを作用させる（ACL準拠）
// vefiry https://onlinejudge.u-aizu.ac.jp/solutions/problem/DSL_2_D/review/11750609/T21140031/C++23
template<class M>
struct DualSegmentTree{
  using FM = function<M(M,M)>;
  ll n,siz,height;
  FM fm;
  const M em;//Mの単位元
  vector<M> lazy;

  DualSegmentTree(ll _n,FM _fm,M _em):n(_n),fm(_fm),em(_em){
    siz = 1;
    height = 0;
    while(siz < n){
      siz <<= 1;
      ++height;
    }
    lazy.resize(2*siz,em);
  }

  DualSegmentTree(vector<M> v,FM _fm,M _em):
    DualSegmentTree((ll)v.size(),_fm,_em){
    for(ll i=0;i<n;i++){
      lazy[siz+i] = v[i];
    }
  }

  void all_apply(ll p,M f){
    lazy[p] = fm(f,lazy[p]);
  }

  void push(ll p){
    all_apply(2*p,lazy[p]);
    all_apply(2*p+1,lazy[p]);
    lazy[p] = em;
  }

  void set(ll p,M x){
    assert(0 <= p && p < n);
    p += siz;
    for(ll i=height;i>=1;i--){
      push(p >> i);
    }
    lazy[p] = x;
  }

  M get(ll p){
    assert(0 <= p && p < n);
    p += siz;
    for(ll i=height;i>=1;i--){
      push(p >> i);
    }
    return lazy[p];
  }

  void apply(ll p,M f){
    assert(0 <= p && p < n);
    p += siz;
    for(ll i=height;i>=1;i--){
      push(p >> i);
    }
    all_apply(p,f);
  }

  void apply(ll l,ll r,M f){
    assert(0 <= l && l <= r && r <= n);
    if(l == r)return;
    l += siz;
    r += siz;

    for(ll i=height;i>=1;i--){
      if(((l >> i) << i) != l)push(l >> i);
      if(((r >> i) << i) != r)push((r-1) >> i);
    }

    while(l < r){
      if(l & 1)all_apply(l++,f);
      if(r & 1)all_apply(--r,f);
      l >>= 1;
      r >>= 1;
    }
  }
};

void solve(){
  LL(n);
  vll a(n);cin >> a;
  if(n == 1){
    cout << max(1LL,a[0]) << endl;
    return ;
  }
  vll num(n+1);
  rep(i,n){
    if(a[i]<=n)num[a[i]]++;
    else num[n]++;
  }
  auto op = [&](ll u,ll v){
    if(u+v >= 1e9){
      return (ll)1e9;
    }
    return u+v;
  };
  ll ng = n+1;//条件を満たさない値
  ll ok = 0;//条件を満たす値
  auto f = [&](ll x)->bool {
    DualSegmentTree<ll> seg(n+1,op,0);
    vll b = num;
    ll need = 0;
    rep(i,x){
      if(i==0){
        need++;
      }else{
        seg.apply(i,i+1,1);
      }
    }
    rrep(i,x-1,1){
      //iを消して調節
      ll v = seg.get(i);
      if(v <= b[i]){
        b[i] -= v;
      }else{
        v -= b[i];
        b[i] = 0;
        seg.apply(0,i,v);
      }
    }
    need += seg.get(0);
    return need <= reduce(all(b));
  };
  while(abs(ok-ng) > 1){
    ll mid = (ok + ng)/2;
    if(f(mid)){
      ok = mid;
    }else{
      ng = mid;
    }
  }
  cout << ok << endl;
}
 
int main(){
  ios::sync_with_stdio(false);cin.tie(nullptr);
  #ifdef DEBUG
    test();
  #else
  LL(t);
  while(t--)
    solve();
  #endif
}