When the Prussians arrived on 2 September, they began a wide encirclement of Paris starting from the southwest which was completed a week later when they had entrenched themselves on all the commanding heights, a front of some . The Prussian force was outnumbered, having some 240,000 men and 1,140 guns, so it was decided not to take the city by direct assault, but by bombarding the garrison into submission. Despite their numerical inferiority, the Prussians were able to defeat several sorties by the garrison; however, supplying sufficient artillery ammunition proved problematic until late in the siege. Eventually, the loss of the Armée de la Loire at the Second Battle of Orléans which was the defender's main hope of relief and the starvation of the civil population resulted in a ceasefire on 26 January 1871 and a surrender two days later.