/* -*- coding: utf-8 -*-
 *
 * 3780.cc:  No.3780 Erase and Mex - yukicoder
 */

#include<cstdio>
#include<algorithm>

using namespace std;

/* constant */

const int MAX_N = 200000;

/* typedef */

using ll = long long;

/* global variables */

int as[MAX_N], cs[MAX_N + 2];

/* subroutines */

bool check(int n, int x) {
  ll c0 = cs[0], d = 1;
  for (int i = n + 1; i > 0; i--) {
    if (i > x) c0 += cs[i];
    else {
      if (cs[i] >= d) c0 += cs[i] - d;
      else d += d - cs[i];
    }
  }
  return c0 >= d;
}

/* main */

int main() {
  int tn;
  scanf("%d", &tn);

  while (tn--) {
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) scanf("%d", as + i);

    if (n == 1) { printf("%d\n", max(1, as[0])); continue; }

    fill(cs, cs + n + 2, 0);
    for (int i = 0; i < n; i++) cs[min(n + 1, as[i])]++;
    
    int x0 = 0, x1 = n;
    while (x0 + 1 < x1) {
      int x = (x0 + x1) / 2;
      if (check(n, x)) x0 = x;
      else x1 = x;
    }
    
    printf("%d\n", x1);
  }

  return 0;
}