while loop issue

[the g-man]

I am taking an intro java summer class and this is one of the assignments. I was going along pretty smoothly with my code until I wrote this for loop and tried to test my progress.

The loop takes in input to create the size of the array of objects. It is for a tournament bracket matchup, so it needs to be 4, 8, 16, 32, or 64. Problem is that when I use || it no longer works.
If I use a statement like while (teamCount != 4) it works fine.

/* Tournament.java
This program takes user input of teams and number of wins to create
an array of team objects and makes pairings of teams for a tournament
@author Gary C. Rogers 2010
*/

import java.util.Scanner;

public class Tournament
{
	public static void main(String[] args)
	{
		int teamCount;
		int teamWins;
		String name;
		
		Scanner input = new Scanner(System.in);
		//Ask the user for thr number of teams for the tournament
		System.out.println("What is the number of teams in the tournament?");
		teamCount = input.nextInt();
		
		//Make sure that the input is valid for matchups
		while (teamCount!=4 || teamCount !=8 || teamCount !=16 || teamCount !=32 || teamCount !=64)
		{
			System.out.println("You have entered an invalid number of teams.  Please try again.");
			
			System.out.println("What is the number of teams in the tournament?");
			teamCount = input.nextInt();
		}

		//Declares the array to store objects
		Team[] teamArray = new Team[teamCount];
		int count = 0;
			
		//Loop allows for the input for the team objects
		do
		{
			System.out.println("What is the team name?");
			name = input.next();
				
			System.out.println("How many wins do they have?");
			teamWins = input.nextInt();
				
			teamArray[count]= new Team( name, teamWins);
			count++;
				
			if (count < teamCount)
			{
				System.out.println("Team information gathered.  Input next team.");
			}
				
			else
			{
				System.out.println("All teams have been inputed.  Thank you.");
			}
		}
			
		while (count < teamCount);
			
		for (int index = 0; index < teamArray.length; index++)
		{
				
			System.out.println(teamArray[index].getTeamName() + " " + teamArray[index].getWins());
				
		}
				
		
		
	}
}

There still needs to be a whole structure written to make the matchups, but for now this displays the team objects that the user inputs.