European Union leaders are gathering in Brussels today to begin tackling their continent's most contentious challenges: how much each country should pay into the Union's common budget after Britain leaves the EU next year, and how the Union's institutions will be organised for the remaining 27 member states.
There is no shortage of potential answers but, as German Chancellor Angela Merkel admitted on the eve of the summit, all will prove to be "very challenging", a diplomatic way of saying that major difficulties lie ahead.
Britain is the second-biggest EU budget contributor, and its departure will leave the Union with a shortfall of around €12 billion (S$19.5 billion) after the end of this decade. The choice facing the remaining member states is clear - they either increase their contributions or cut the budget.
In practice, matters are more difficult, since a recent study by the European Parliament points out that Brexit "does not just increase the financial burden for the EU 27, but also changes the distribution of that burden" between remaining member states.
Because of the way Europe's complicated financial arrangements work - with contributions calculated according to a country's size but expenditure distributed according to member states' needs - Germany, already Europe's single biggest financial backer, will also be on the hook for the biggest rise in extra contributions from 2020.
Germany's present net financial contribution - calculated as the total money transferred to Brussels, minus the money Germany receives back in EU-funded projects - amounts to €15.6 billion a year; if current financial arrangements remain in place, the Germans will be asked for an extra €3.8 billion annually.
France, which becomes the EU's second-largest economy after the British depart, will be expected to pay only an extra €1.2 billion a year, and Italy only an additional €1 billion.
Dr Merkel has already signalled her readiness to pay up, and Mr Guenther Oettinger - the EU official responsible for the common budget, who is himself both German and close to Dr Merkel - has tried to make light of this expected extra contribution.
"That would be only about 10 euro cents per day more than now, for each German," said Mr Oettinger.
Still, the sums involved are large and Dr Merkel, who now exercises far weaker political control at home, cannot be seen to be making immediate concessions, so the Germans refuse to say just how deep they may be prepared to dig into their national pockets.
Dr Merkel's room for manoeuvre is further restricted by the fact that a number of other prosperous EU states are simply refusing to increase their own contributions.
Mr Mark Rutte, the Netherlands' Prime Minister, has already said that his country will not pay more, and similar objections have been received in private from Sweden, Austria, Finland and Denmark - enough nations to derail the entire budget process.
Meanwhile, the option of simply cutting the EU budget is also deeply controversial. The former communist states of Central and Eastern Europe, considerably poorer than their western counterparts, are certain to oppose it; they are demanding both an increase in EU spending and a further diversion of funds to the east in order to eliminate the continent's economic disparities.
European leaders are also expected to deal with another divisive matter today - the selection of the next president of the EU Commission, the Union's executive body. Historically, the president was appointed by leaders of the member states, usually after a backroom deal struck between Germany and France.
However, current EU Commission president Jean-Claude Juncker got his job through a different route - by topping the list of all the centre-right European political parties which competed in the last European Parliament elections in 2014 and by claiming that, since his grouping won that election, he was entitled to become commission president.
The 63-year-old Mr Juncker, who is standing down next year, wants to make this "top of the list" arrangement permanent by getting governments to agree to follow the same procedure in the EU parliamentary elections scheduled for May next year. "When we go to the polls, we know who can be the future president," he argued.
But French President Emmanuel Macron leads a group of EU leaders opposed to giving up their sovereign right to choose who will head the EU Commission, at least not before conducting a broader discussion about the distribution of power in the EU.
As always in Europe, a compromise of sorts will emerge after further haggling. But it is already clear that Britain's departure from the EU will continue to have a profound impact on the rest of the continent for many years to come.
