The French gained access to the outermost ward by undermining its advanced main tower. Following this, Philip ordered a group of his men to look for a weak point in the castle. They gained access to the next ward when a soldier named Ralph found a latrine chute in use through which the French could clamber into the chapel. After ambushing several unsuspecting guards, and setting fire to the buildings, Philip's men then lowered the movable bridge and allowed the rest of their army into the castle. The Anglo-Norman troops retreated to the inner ward. After a short time the French successfully breached the gate of the inner ward, and the garrison retreated finally to the keep. With supplies running low Roger de Lacy and his garrison of 20 knights and 120 other soldiers surrendered to the French army, bringing the siege to an end on 6 March 1204. In drawn-out medieval sieges, contemporary writers often emphasised the importance of dwindling supplies in the capitulation of the garrison, as was the case with the Siege of Château Gaillard. With the castle under French control, the main obstacle to the French entering the Seine valley was removed; they were able to enter the valley unmolested and take Normandy. Thus, for the first time since it had been given as a duchy to Rollo in 911, Normandy was directly ruled by the French king. The city of Rouen surrendered to Philip II on 23 June 1204. After that, the rest of Normandy was easily conquered by the French.