#nullable enable

static int Solve()
{
    var n = int.Parse(Console.ReadLine()!);
    var az = Console.ReadLine()!.Split(' ').Select(int.Parse).ToArray();

    bool J(int k)
    {
        var cz = new int[k];
        foreach (var a in az)
        {
            if (a < k) cz[a]++;
            else cz[0]++;
        }
        var d = 0;
        for (var i = k - 1; i > 0; i--)
        {
            var c = cz[i];
            if (c > d) cz[0] += c - d - 1;
            else
            {
                d += d - c + 1;
                if (d > n) return false;
            }
        }
        return cz[0] > d;
    }

    var pass = 0;
    var fail = n + 2;
    while (fail - pass >= 2)
    {
        var mid = (pass + fail) >> 1;
        if (J(mid)) pass = mid;
        else fail = mid;
    }
    return pass;
}

var t = int.Parse(Console.ReadLine()!);
var ans = Enumerable.Range(0, t).Select(_ => Solve()).ToArray();
Console.WriteLine(string.Join(Environment.NewLine, ans));