var SpatialGrid = Container.expand(function (cellSize) {
	var self = Container.call(this);
	self.cellSize = cellSize;
	self.grid = {};
	self._cellKey = function (x, y) {
		var cellX = Math.floor(x / self.cellSize);
		var cellY = Math.floor(y / self.cellSize);
		return cellX + ':' + cellY;
	};
	self.insert = function (object) {
		var key = self._cellKey(object.x, object.y);
		if (!self.grid[key]) {
			self.grid[key] = [];
		}
		self.grid[key].push(object);
	};
	self.retrieve = function (x, y) {
		var key = self._cellKey(x, y);
		return self.grid[key] || [];
	};
	self.clear = function () {
		self.grid = {};
	};
});
var Hero = Container.expand(function () {
	var self = Container.call(this);
	var heroGraphics = self.createAsset('hero', 'Hero character', .5, .5);
	self.move = function () {};
	self.shoot = function () {};
});
var EnemyWave0 = Container.expand(function (enemyCount) {
	var self = Container.call(this);
	self.enemyCount = 1;
	var enemyGraphics = self.createAsset('enemyWave0', 'Enemy Wave 0 character', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		var speed = 1;
		var newX = this.x + dx / magnitude * speed;
		var newY = this.y + dy / magnitude * speed;
		var goalX = 2048 / 2;
		var goalY = goal.height / 2;
		var goalWidth = goal.width;
		var goalHeight = goal.height;
		this.x = Math.max(goalX - goalWidth / 2, Math.min(goalX + goalWidth / 2, newX));
		this.y = Math.max(goalY - goalHeight / 2, Math.min(goalY + goalHeight / 2, newY));
	};
});
var EnemyWave1 = Container.expand(function (enemyCount) {
	var self = Container.call(this);
	self.enemyCount = 10;
	var enemyGraphics = self.createAsset('enemyWave1', 'Enemy Wave 1 character', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		var speed = 2.5;
		this.x += dx / magnitude * speed;
		this.y += dy / magnitude * speed;
	};
});
var EnemyWave2 = Container.expand(function (enemyCount) {
	var self = Container.call(this);
	self.enemyCount = 3;
	var enemyGraphics = self.createAsset('enemyWave2', 'Enemy Wave 2 character', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		var speed = 2;
		this.x += dx / magnitude * speed;
		this.y += dy / magnitude * speed;
	};
});
var EnemyWave3 = Container.expand(function (enemyCount) {
	var self = Container.call(this);
	self.enemyCount = 4;
	var enemyGraphics = self.createAsset('enemyWave3', 'Enemy Wave 3 character', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		var speed = 1.8;
		this.x += dx / magnitude * speed;
		this.y += dy / magnitude * speed;
	};
});
var EnemyWave4 = Container.expand(function (enemyCount) {
	var self = Container.call(this);
	self.enemyCount = 20;
	var enemyGraphics = self.createAsset('enemyWave4', 'Enemy Wave 4 character', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		var speed = 3;
		this.x += dx / magnitude * speed;
		this.y += dy / magnitude * speed;
	};
});
var EnemyWave5 = Container.expand(function (enemyCount) {
	var self = Container.call(this);
	self.enemyCount = 1;
	var enemyGraphics = self.createAsset('enemyWave5', 'Enemy Wave 5 character', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		var speed = 10;
		this.x += dx / magnitude * speed;
		this.y += dy / magnitude * speed;
	};
});
var HeroBullet = Container.expand(function () {
	var self = Container.call(this);
	var bulletGraphics = self.createAsset('heroBullet', 'Hero Bullet', .5, .5);
	self.move = function (goalX, goalY) {
		var dx = goalX - this.x;
		var dy = goalY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		this.x += dx / magnitude * 5;
		this.y += dy / magnitude * 5;
	};
});
var EnemyBullet = Container.expand(function () {
	var self = Container.call(this);
	var bulletGraphics = self.createAsset('enemyBullet', 'Enemy Bullet', .5, .5);
	self.move = function (heroX, heroY) {
		var dx = heroX - this.x;
		var dy = heroY - this.y;
		var magnitude = Math.sqrt(dx * dx + dy * dy);
		this.x += dx / magnitude * 2;
		this.y += dy / magnitude * 2;
	};
});
var Game = Container.expand(function () {
	var self = Container.call(this);
	self.getEnemyCountForWave = function (waveIndex) {
		switch (waveIndex % 6) {
			case 0:
				return 1;
			case 1:
				return 10;
			case 2:
				return 3;
			case 3:
				return 4;
			case 4:
				return 20;
			case 5:
				return 1;
		}
	};
	var goal = self.createAsset('goal', 'Goal asset', 0.5, 0.5);
	goal.width = 900;
	goal.height = 200;
	goal.x = 2048 / 2;
	goal.y = goal.height / 2;
	self.addChild(goal);
	var hero = self.addChild(new Hero());
	var enemies = [];
	var waveIndex = 0;
	var maxWaveCount = 6;
	var waveTimer = 500;
	var waveInterval = 500;
	var heroBullets = [];
	var enemyBullets = [];
	hero.x = 2048 / 2;
	hero.y = 2732 / 2;
	var bulletTimer = 0;
	var bulletInterval = 100;
	LK.on('tick', function () {
		hero.move();
		bulletTimer++;
		if (bulletTimer >= bulletInterval) {
			var newBullet = new HeroBullet();
			newBullet.x = hero.x;
			newBullet.y = hero.y;
			heroBullets.push(newBullet);
			self.addChild(newBullet);
			bulletTimer = 0;
		}
		if (waveIndex < maxWaveCount) {
			waveTimer++;
		}
		if (waveTimer >= waveInterval && waveIndex < maxWaveCount) {
			for (var i = 0; i < self.getEnemyCountForWave(waveIndex); i++) {
				var newEnemy;
				var enemyCount = self.getEnemyCountForWave(waveIndex);
				switch (waveIndex % 6) {
					case 0:
						newEnemy = new EnemyWave0(enemyCount);
						newEnemy.x = 1000;
						newEnemy.y = 0;
						break;
					case 1:
						newEnemy = new EnemyWave1(enemyCount);
						newEnemy.x = Math.random() * 2048;
						newEnemy.y = 0;
						break;
					case 2:
						newEnemy = new EnemyWave2(enemyCount);
						newEnemy.x = Math.random() * 2048;
						newEnemy.y = 2732;
						break;
					case 3:
						newEnemy = new EnemyWave3(enemyCount);
						newEnemy.x = 2048;
						newEnemy.y = Math.random() * 2732;
						break;
					case 4:
						newEnemy = new EnemyWave4(enemyCount);
						newEnemy.x = 0;
						newEnemy.y = Math.random() * 2732;
						break;
					case 5:
						newEnemy = new EnemyWave5(enemyCount);
						newEnemy.x = 1000;
						newEnemy.y = 0;
						break;
				}
				enemies.push(newEnemy);
				self.addChild(newEnemy);
			}
			waveIndex++;
			waveTimer = 0;
		}
		var spatialGrid = new SpatialGrid(100);
		for (var i = 0; i < enemies.length; i++) {
			spatialGrid.insert(enemies[i]);
		}
		for (var i = 0; i < enemies.length; i++) {
			var enemy = enemies[i];
			var nearbyEnemies = spatialGrid.retrieve(enemy.x, enemy.y);
			enemy.move(hero.x, hero.y);
			if (enemy.intersects(hero)) {
				LK.showGameOver();
				return;
			}
			for (var j = 0; j < nearbyEnemies.length; j++) {
				var otherEnemy = nearbyEnemies[j];
				if (otherEnemy !== enemy && enemy.intersects(otherEnemy)) {
					var overlapX = enemy.x - otherEnemy.x;
					var overlapY = enemy.y - otherEnemy.y;
					var overlapMagnitude = Math.sqrt(overlapX * overlapX + overlapY * overlapY);
					if (overlapMagnitude < 50) {
						enemy.x += overlapX / overlapMagnitude;
						enemy.y += overlapY / overlapMagnitude;
					}
				}
			}
		}
		spatialGrid.clear();
		for (var i = 0; i < heroBullets.length; i++) {
			heroBullets[i].move(goal.x, goal.y);
			for (var j = 0; j < enemies.length; j++) {
				if (heroBullets[i].intersects(enemies[j])) {
					heroBullets[i].destroy();
					heroBullets.splice(i, 1);
					break;
				}
			}
		}
		for (var i = 0; i < enemyBullets.length; i++) {
			enemyBullets[i].move();
		}
	});
	stage.on('move', function (obj) {
		var pos = obj.event.getLocalPosition(self);
		hero.x = pos.x;
		hero.y = pos.y;
	});
});

===================================================================
--- original.js
+++ change.js
@@ -36,10 +36,16 @@
 		var dx = heroX - this.x;
 		var dy = heroY - this.y;
 		var magnitude = Math.sqrt(dx * dx + dy * dy);
 		var speed = 1;
-		this.x += dx / magnitude * speed;
-		this.y += dy / magnitude * speed;
+		var newX = this.x + dx / magnitude * speed;
+		var newY = this.y + dy / magnitude * speed;
+		var goalX = 2048 / 2;
+		var goalY = goal.height / 2;
+		var goalWidth = goal.width;
+		var goalHeight = goal.height;
+		this.x = Math.max(goalX - goalWidth / 2, Math.min(goalX + goalWidth / 2, newX));
+		this.y = Math.max(goalY - goalHeight / 2, Math.min(goalY + goalHeight / 2, newY));
 	};
 });
 var EnemyWave1 = Container.expand(function (enemyCount) {
 	var self = Container.call(this);
@@ -154,9 +160,9 @@
 	self.addChild(goal);
 	var hero = self.addChild(new Hero());
 	var enemies = [];
 	var waveIndex = 0;
-	var maxWaveCount = 5;
+	var maxWaveCount = 6;
 	var waveTimer = 500;
 	var waveInterval = 500;
 	var heroBullets = [];
 	var enemyBullets = [];