A_Maximum_Square.cpp

// Neepan Biswas
// neepanb ~ codeforces
#include <bits/stdc++.h>
using namespace std;

#define fr(i, n) for (lli i = 0; i < n; i++)
#define pb push_back
#define sz(x) x.size()
#define ff first
#define ss second
#define all(v) v.begin(), v.end()
#define debug(x) cout << '>' << #x << ':' << x << endl;
#define cd(condition, value_if_true, value_if_false) ((condition) ? (value_if_true) : (value_if_false))

using lli = long long int;
using ld = long double;
using pi = pair<lli, lli>;
using vp = vector<pi>;
using vi = vector<lli>;
using bl = bool;
using mp = map<lli, lli>;
using ump = unordered_map<lli, lli>;
using str = string;

#pragma GCC optimize("unroll-loops,O3,Ofast")
#pragma GCC target("avx2,avx,fma,bmi,bmi2,lzcnt,popcnt")


bool canFormSquare(const vi &a, lli sideLength) {
    lli count = 0;
    for (lli i = a.size() - 1; i >= 0 && count < sideLength; --i) {
        if (a[i] >= sideLength) {
            ++count;
        }
    }
    return count >= sideLength;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    lli t;
    cin >> t;

    while (t--)
    {
        lli n;
        cin >> n;
        vi a(n);
        fr(i, n) cin >> a[i];
        if (n == 1)
        {
            cout<< 1 << endl;
        }
        else
        {
           sort(all(a));
            lli low = 1, high = n, result = 1;
            while (low <= high) {
                lli mid = (low + high) / 2;
                if (canFormSquare(a, mid)) {
                    result = mid;
                    low = mid + 1;
                } else {
                    high = mid - 1;
                }
            }
            cout << result << endl;
        }
        
    }
    return 0;
}