Simple 2D Random walk

I'm having a problem with average distance in this exercise. It should be close to the sqrt of N steps, but it's lower. Can you help me to find out where is my mistake?

2D random walk. A two dimensional random walk simulates the behavior of a particle moving in a grid of points. At each step, the random walker moves north, south, east, or west with probability 1/4, independently of previous moves. Determine how far away (on average) the random walker is from the starting point after N steps. (Theoretical answer: on the order of sqrt(N).)

public class RandomWalk{
    public static void main(String[] args){

    int N = Integer.parseInt(args[0]);

    double nextStep = 0;
    double averageDistance = 0;
    int COUNT = 1000;

    for (int j = 0; j < COUNT; j++){
        int moveWest = 0;
        int moveEast = 0;
        int moveSouth = 0;
        int moveNorth = 0;
        double distance = 0;

        for (int i = 0; i < N; i++){
        nextStep = Math.random()*4;
        if (nextStep <= 1) ++moveWest;
          else if (nextStep <= 2) ++moveEast;
            else if (nextStep <= 3) ++moveSouth;
              else if (nextStep <= 4)++moveNorth;       
        }

        moveEast = moveEast - moveWest;
        moveNorth = moveNorth - moveSouth;
        distance = Math.sqrt((moveEast * moveEast) + (moveNorth * moveNorth));
        averageDistance += distance; 

        System.out.println("Walker is " + distance + "\t steps away of from the starting point");
        //System.out.println("Sqrt of N is " + Math.sqrt(N));

    }
    System.out.println("Average distance is " + averageDistance/COUNT + " steps away of from the starting point");
    }
}