Won't output array list.

Hello I'm having trouble with my program. I have a couple of problems. First of all, the program won't output the name, id, and gpa. It comes out as a blank. Second of all, when I enter the amount of students that I want in the array based list, it keeps on going after it reaches that number. I'm very lost. Thank you in advance for your help.

#include <iomanip>
#include <iostream>
#include <string>
using namespace std;

struct Student
{
  string name;
  int id;
  float gpa;
};

void printStudents(Student* student, int nStudents)
{
  int i;
  for(i=0;i < nStudents; i++)
  {
    cout << "Name = " << left << setw(30) << student[i].name;
	cout.fill('0');
	cout << " ID = " << right << setw(7)
	  << student[i].id << ", gpa = "
	  << student[i].gpa << endl;
	cout.fill(' ');
  }
}

int main()
{
  const int MAX_STUDENTS = 100;  //Capacity
  int nStudents = 0;
  Student student[MAX_STUDENTS];
  
  while(true)
  {
  // Get how many students.
  cout << "How many students are there? : ";
  cin >> nStudents;
  cin.ignore(1000,10);
  
  if(nStudents == 0)
    break;
  
  // Get and save the records.
  for( int i=0; i < nStudents; i++)
  {
    Student aStudent;
	
	cout << "Name: " << endl;
	getline(cin, aStudent.name);
	
	cout << "ID: " << endl;
	cin >> aStudent.id;
	cin.ignore(1000,10);
	
	cout << "GPA: " << endl;
	cin >> aStudent.gpa;
	cin.ignore(1000,10);
	
	if(nStudents < MAX_STUDENTS)
	  student[nStudents++] = aStudent;
	
  }
  
  //Sort by gpa.
  for(int i=0; i < nStudents; i++)
  {
    for(int j=1 + i; j < nStudents; j++)
	{
	  if (student[i].gpa > student[j].gpa)
	  {
	    Student temp = student[i];
		student[i] = student[j];
		student[j] = temp;
	  }
	}
  }
  
  printStudents(student, nStudents);
  }
  if(nStudents == 0)
    cout << "No students were added." << endl;
}