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//var url = "https://www.youtube.com/embed/SG-nqVOw_BY";
var url = "https://www.youtube.com/watch?v=SG-nqVOw_BY";

if (url.indexOf("watch") >= 0) {
	url = url.split('?v=')
  url = 'https://www.youtube.com/embed/' + url[1]
}

$('#output').html(url)

<p id = "output"></p>