WordPress: Loop through 3 most recent posts from each category

3-recent-posts.php

<?php
/**
 * Loop through 3 most recent posts from each category
 * @see http://codex.wordpress.org/Function_Reference/get_categories
 */
$do_not_duplicate = array();
$categories = get_categories();
foreach ( $categories as $category ) :

	$args = array(
		'cat'            => $category->term_id,
		'post_type'      => 'post',
		'posts_per_page' => 3,
		'post__not_in'   => $do_not_duplicate
	);

	$query = new WP_Query( $args );

	if ( $query->have_posts() ) : ?>

		<div class="row">
			<div class="col-sm-12">
				<h3 class="cat-title"><?php echo $category->name; ?><span></span></h3>
			</div>
		</div>

			<?php
			while ( $query->have_posts() ) :

				$query->the_post();
				$do_not_duplicate[] = get_the_id();
				?>

				<div id="post-<?php the_ID(); ?>" <?php post_class( 'row category-listing' ); ?>>
					<div class="col-sm-2">
						<div class="datebox">
							<div class="day"><?php the_time('j'); ?></div>
			 				<div class="monthyear"><?php the_time('M, Y'); ?></div>
						 </div>
					</div>
					<div class="col-sm-10">
						<h3 class="entry-title">
							<a href="<?php the_permalink(); ?>"><?php the_title(); ?></a>
						</h3>

						<div class="cat-name">
							<?php echo $category->name; ?>
						</div>

						<?php the_excerpt(); ?>

						<a class="pull-right read-more" href="<?php the_permalink(); ?>">Read More <i class="fa fa-angle-right"></i></a>
					</div>
				</div>

			<?php endwhile; wp_reset_postdata(); ?>

			<div class="row cat-read-all">
				<div class="col-sm-12">
					<a class="pull-right" href="<?php echo get_category_link( $category->term_id ); ?>">Read All <?php echo $category->name; ?></a>
				</div>
			</div>

	<?php endif;

endforeach;

Is there a way to show only 6 posts? I have 200 categories and don't want to show 600 post. I only need the 6 newest from 200 categories and max one of each category.