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The Rossoneri, who need only a point from their Dutch counterparts to book their place in the second round of the competition, face an uphill task in their bid to seal progression, though, as Riccardo Montolivo's 22nd-minute red card handed the Dutch a numerical advantage.
Frank de Boer's men, who need all three points to progress at the expense of Milan, came within the width of the post from taking a fifth-minute lead.
Christian Poulsen rose highest from a Lasse Schone corner but the Dane saw his header cannon off the post.
Montolivo was soon dismissed for a late challenge on Poulsen to give Massimiliano Allegri's men a testing second half.