What do the Bolsonaro protesters in Brazil want?

Brazilians have woken up today still processing what on earth went on in their country's capital on Sunday.

The scenes of chaos shouldn't have come as a surprise, though.

Throughout Jair Bolsonaro's term, he has repeatedly questioned the efficacy of Brazil's institutions - accusing the Supreme Federal Court of being politically against him, and the voting system of being prone to fraud, despite no evidence to support those claims.

In short, he may not have masterminded the invasion, but he cannot be separated from it. His supporters took on his narrative wholeheartedly.

Since he lost the elections in October, Mr Bolsonaro has gone very quiet. He has not publicly conceded defeat - he flew off to Florida to avoid having to hand over the presidential sash to Lula - and he's allowed his most ardent supporters to remain angry over a democratic election that he legitimately lost.

Last week, his former vice president said the silence of leaders sowed chaos in society - and that is what Jair Bolsonaro is guilty of, at the very least.

Tension has definitely been building these past few months. Camps were set up across the country in front of army headquarters, with protesters loyal to Mr Bolsonaro calling for military intervention.

And then in December, supporters set fire to Federal Police headquarters in Brasilia. Another supporter was arrested for allegedly trying to set off a bomb before Lula's inauguration on 1 January.

Brazilians feared what happened on Sunday was only a matter of time. Perhaps more worrying is the role the authorities played in allowing this to happen.

It's no secret that many security forces are more on the side of Mr Bolsonaro than Lula. Mr Bolsonaro's narrative throughout his term about security in Brazil - and keeping people safe - made sure he had allies within the police and the armed forces.

Brasilia's governor, Ibaneis Rocha - a long-time ally of Jair Bolsonaro - has been suspended for 90 days. The Security Secretary of Brasilia, Anderson Torres, was also dismissed over yesterday's events.

To what point, then, were authorities working with protesters to allow such an invasion of top-security government buildings?

And pressure is building outside Brazil too - with Mr Bolsonaro still in Florida, Joe Biden has already been asked to extradite the former Brazilian president to face questions back home.

While Lula's administration tries to get to the bottom of where it all went wrong, the challenge remains - he has formidable opposition in these protesters, so could this happen again?

While much has been said about the protesters' anger over Mr Bolsonaro's loss in October, this is more about the man he lost to - Lula.

For them, the current president - who was jailed in 2017 for corruption, and spent 18 months in prison before the convictions were annulled - is a corrupt politician who belongs in prison, not the presidential palace.

They falsely accuse him of being a communist, wanting to impose a regime like Venezuela or Cuba. They won't be convinced by anything else - and they won't give up their fight for "democracy" as they call it.

But there's a massive flaw in their argument in wanting freedom and democracy.

They are calling for a very undemocratic military intervention to "save" Brazil - an intervention that despite their best efforts, doesn't look forthcoming.