public class Solution {
    private record struct ClassRecord(int Passes, int Students) {
        public double PassRatio => (double)Passes / Students;
        public double Gain => (double)(Passes + 1) / (Students + 1) - PassRatio;
    }

    public double MaxAverageRatio(int[][] classes, int extraStudents) {
        // Construct the max heap based on the effect of adding student
        var q = new PriorityQueue<ClassRecord, double>();
        foreach (var classRecord in classes) {
            var c = new ClassRecord(classRecord[0], classRecord[1]);
            q.Enqueue(c, -c.Gain);
        }

        // Add the students based on priority
        while (extraStudents-- > 0) {
            var c = q.Dequeue();

            var cWithNewStudent = new ClassRecord(c.Passes + 1, c.Students + 1);
            q.Enqueue(cWithNewStudent, -cWithNewStudent.Gain);
        }

        // Calculate final pass ratio
        double ratio = 0;
        while (q.TryDequeue(out var c, out var gain)) {
            ratio += c.PassRatio;
        }

        return ratio / classes.Length;
    }
}