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<?php
/* DON'T copy the first line (above) if your functions.php already has it. 
 * ---------------------------------------------------------------------- */

// customize oEmbed URL's query string (such as adding rel=0)
function my_custom_youtube_oembed_settings( $html, $url='', $attr='', $post_ID='' ) {
    if ( strpos( $html, 'youtu.be' ) !== false || strpos( $html, 'youtube.com' ) !== false ) {
    	if ( strpos( $html, 'autoplay' ) === false ) {
        	$return = preg_replace( "@src=(['\"])?([^'\">\s]*)@", "src=$1$2&rel=0&autoplay=1", $html );
        	return $return;
    	}
    }
    return $html;
}
add_filter('embed_handler_html', 'my_custom_youtube_oembed_settings', 10, 3);
add_filter('embed_oembed_html', 'my_custom_youtube_oembed_settings', 10, 3);
add_filter('oembed_result', 'my_custom_youtube_oembed_settings');