Lai represents an historic third term in power for the pro-sovereignty Democratic Progressive party (DPP)

• Who is Lai Ching-te?
• Taiwan’s new president to take office
• See all of our Taiwan coverage

The Guardian’s Helen Davidson and Chi Hui Lin are at the inauguration in Taipei. They have this report:

It is a sea of bucket hats outside the Presidential Office.

Helicopter carrying Raisi and foreign minister Hossein Amir-Abdollahian reportedly crashed in mountainous area amid bad weather

• Full report: helicopter carrying Iran’s president crashes in mountains
• Profile: Ebrahim Raisi: Iran’s hardline president dogged by execution claims

Iranians have been praying for the president, while expressions of concern come in from around the world

One Tehran citizen, a 29-year-old journalist who only gave her name as Vakili, told the news agency AFP she “feared” the worst and said it recalled previous tense moments in recent years.

Six people killed and dozens wounded after two waves of strikes on resort on edge of city, with more attacks in wider region killing five. What we know on day 817

• See all our Ukraine war coverage

Russia struck a lakeside resort on the edge of Kharkiv on Sunday and attacked villages in the surrounding region, killing at least 11 people and wounding scores. Prosecutors said six people were killed in the resort, with one missing and 27 wounded. Rescuers said the initial strike was followed by a second strike about 20 minutes later, targeting emergency crews at the scene in a “double tap”. “There were never any soldiers here,” said Yaroslav Trofimko, a police inspector who arrived after the first strike and was then caught up in the second. Another five people were killed and nine injured later in the day in two villages in Kupiansk district. Local governor Oleh Syniehubov said Russian forces shelled two villages of the district with a self-propelled multiple rocket launcher. Prosecutors said one person was killed in Russian shelling in the town of Vovchansk, a town at the centre of a Russian incursion launched just over a week ago. Three people were wounded. The missile strikes were the latest in what have been constant Russian attacks in recent weeks on the Kharkiv region of north-eastern Ukraine, where Russian troops have launched an offensive.

Britain and Finland will sign a strategic partnership on Monday to strengthen ties and counter the threat of Russian aggression, UK foreign secretary David Cameron has said. The two countries will declare Russia as “the most significant and direct threat to European peace and stability”, according to a Foreign Office press release. “As we stand together to support Ukraine, including through providing military aid and training, we are clear that the threat of Russian aggression, following the war it started, will not be tolerated,” said Cameron. The countries will work together to counter Russian disinformation, malicious cyber activities and support Ukraine’s recovery, reconstruction, and modernisation, according to the Foreign Office.

Ukrainian president Volodymyr Zelenskiy said Ukraine’s armed forces have strengthened their positions in Kharkiv this week and that they were “effectively destroying” occupying forces in Donetsk region, particularly near Chasiv Yar. “In fact, the occupiers fail to achieve their goal of stretching our forces thin and weakening Ukraine across a wide front from the Kharkiv to the Donetsk regions,” he said.

The Ukrainian military shelled areas of Russia’s southern Belgorod region on Sunday, injuring at least 13 people and damaging dwellings, regional governor Vyacheslav Gladkov said. Gladkov wrote on Telegram that multiple-launch rockets hit the town of Shebekino, injuring 11 people, including three children. Seven apartment buildings sustained damage. On the town’s eastern fringe, in the village of Rzhevka, two people were injured in shelling by the Ukrainian military, Gladkov said. At least one dwelling was badly damaged. The reports could not be independently verified. Ukraine has staged frequent attacks on towns and villages on Russian regions on its border.

All five systems tested were found to be ‘highly vulnerable’ to attempts to elicit harmful responses

Guardrails to prevent artificial intelligence models behind chatbots from issuing illegal, toxic or explicit responses can be bypassed with simple techniques, UK government researchers have found.

The UK’s AI Safety Institute (AISI) said systems it had tested were “highly vulnerable” to jailbreaks, a term for text prompts designed to elicit a response that a model is supposedly trained to avoid issuing.

Ability to preserve tissue in a special gel solution for at least a week will help doctors identify most effective drug treatments

Scientists say they have a made a potentially “gamechanging” breakthrough in breast cancer research after discovering how to preserve breast tissue outside the body for at least a week.

The study, which was funded by the Prevent Breast Cancer charity, found tissue could be preserved in a special gel solution, which will help scientists identify the most effective drug treatments for patients.

‘More than three years after end of transition period, it is still not clear when full controls will be in place’

Post-Brexit border checks will cost UK businesses £470m a year, the government’s public spending watchdog has said.

Plans to bring in border checks on goods coming from the EU faced “significant issues” including critical shortages of inspectors before their introduction last month, the National Audit Office said in a report.

• American makes a birdie at final hole to claim a first major
• Bryson DeChambeau second on -20; Victor Hovland third

It seemed appropriate that this staging of the US PGA Championship played out in the home city of Muhammad Ali. Viktor Hovland swung and missed at Xander Schauffele all afternoon. Bryson DeChambeau, with typical force, did likewise. Schauffele is golf’s nearly man no more. He withstood immense pressure to claim the Wanamaker Trophy.

Bare statistics disguise epic sporting theatre during what quickly became a three-horse sprint. Schauffele, at 21 under par, saw off DeChambeau by one, breaking the record score to par in majors by the same margin. Hovland, such an integral part of the Valhalla story, closed at minus 18.

Cannes film festival
Moore plays a fading Hollywood star whose career is set to be axed by misogynists when she’s offered a secret new medical procedure

Coralie Fargeat, known for the violent thriller Revenge from 2017, now cranks up the amplifier for some death metal … or nasty injury metal anyway. This is a cheerfully silly and outrageously indulgent piece of gonzo body-horror comedy, lacking in subtlety, body-positivity or positivity of any sort. Roger Corman would have loved it. It’s flawed and overlong but there’s a genius bit of casting in Demi Moore who is a very good sport about the whole thing. And as confrontational satire it strikes me as at least as good, or better, than two actual Palme d’Or winners: Julia Ducournau’s Titane and Ruben Östlund’s Triangle of Sadness.

The Substance is a grisly fantasy-parable of misogyny and body-objectification, which riffs on the crazy dysfunctional energy of Roger Vadim and Jane Fonda with borrowings from Frankenheimer and Cronenberg. It’s about successful careers for women in the media and public life being contingent on being forced to keep another, older, less personable self locked away. But unlike Dorian Gray’s portrait, this can’t simply be forgotten about, but continually tended to. Fargeat saves up an awful reckoning for an odious media executive called Harvey, but in an interesting way locates her horror in women’s own fear of their younger and older selves.

• Indiana Pacers 130-109 New York Knicks
• Pacers advance with historic shooting performance
• Knicks hit hard by injuries as they crash out

Tyrese Haliburton scored 26 points and the Indiana Pacers rode one of the most sensational first halves in Game 7 history to a 130-109 victory over the New York Knicks on Sunday, advancing to the Eastern Conference finals for the first time in 10 years.

The Pacers made 29 of their 38 shots in the first half, a shooting percentage of 76.3%. That was the highest in the postseason since 1997, when the NBA began keeping detailed play-by-play for all four quarters. They led 70-55 at that point and pulled away every time the Knicks tried to make a run in the second half.

Costner writes, directs and stars alongside Sienna Miller and Sam Worthington in a big vain slog up familiar old west alleys

After three saddle-sore hours, Kevin Costner’s handsome-looking but oddly listless new western doesn’t get much done in the way of satisfying storytelling.

Admittedly, this is supposed to be just the first of a multi-part saga for which Costner is director, co-writer and star. But it somehow doesn’t establish anything exciting for its various unresolved storylines, and doesn’t leave us suspensefully hanging for anything else.

In fact, the ploddingly paced epic ends by suddenly accelerating into a very peculiar preview montage of part two, with Costner speeding around punching people we’ve never seen before – as if someone had accidentally leant on the fast-forward button and we got to watch the whole of the second section in 25 seconds.

It certainly starts at a gallop. The various plot strands in Montana, Wyoming and Kansas entwine around a new white pioneer settlement in the 1860s American west, called Horizon, attracting any number of hardy or naive souls who don’t know or haven’t been told that the Apaches will not surrender this territory without a fight.

After a mysterious attempted slaying of a man in a remote shack (the storyline which is subject to the most conspicuously deferred explanation) we witness, on one terrible night, apaches attacking the Horizon settlement and burning it to the ground, killing many, and making a widow of a homesteader’s wife: Frances (Sienna Miller) leaving her children fatherless. It is a genuinely gripping sequence.

A retaliatory raiding party is organised by vindictive trackers who don’t care if they capture the actual apaches responsible – just any native Americans – to get the bounty cash. They are reluctantly permitted to do by the Unionist soldiers, exasperated by the existence of the Horizon township which is situated in open country almost impossible for them to defend.

They are led by modest, handsome First Lt Trent Gephardt (Sam Worthington) who supposedly experiences a romantic connection with Frances – and Miller has to pivot her character on a dime from the grief and horror of seeing her husband killed, to a state of simpering, skittish flirting with hunky Trent.

Meanwhile, the apaches are deeply divided about how to handle the thread from the settlers; hotheaded young Pionsenay (Owen Crow Shoe) is furious at his father’s lack of direct action.

Another plot strand has a gruelling wagon train led by Matthew Van Weyden (Luke Wilson) having to deal with food and water shortages, the ever-present risk of attack and a couple of lazy entitled Brits who won’t pull their weight.

Coup leader killed and 50 people, including Americans, arrested after men reportedly attacked presidency in capital Kinshasa

The leader of an attempted coup on Sunday in the Democratic Republic of Congo (DRC) has been killed and some 50 people including three American citizens arrested, a spokesperson for the Central African country’s army told Reuters.

Gunfire rang out around 4am in the capital Kinshasa, a Reuters reporter said. Armed men attacked the presidency in the city centre, according to spokesperson Sylvain Ekenge.

• Manager’s contract will expire at the end of next season
• Catalan has won six Premier League titles in the last seven years

Pep Guardiola admitted next season may be his last as Manchester City manager after the club made history as the first team since the inception of the Football League in 1888 to claim four consecutive titles, following a 3‑1 victory against West Ham.

Guardiola, who was close to tears when talking about Jürgen Klopp’s departure as Liverpool manager, he also revealed that he initially struggled for motivation following the ­treble triumph last season that was confirmed by winning the ­Champions League final in Turkey.

• ‘If we do what we have to do, we will get closer, and we will win it’
• Arsenal miss out to Manchester City on Premier League final day

Mikel Arteta has pledged Arsenal will rejoin battle with Manchester City for the Premier League title next season and “bare our teeth” as they seek to further shrink the closing gap between the teams.

A 2-1 win against Everton was not enough for the Gunners on Sunday after City beat West Ham to win the league by two points. After taking the title race to the final day, however, the Arsenal manager said he was ready to redouble his efforts to overhaul what he called the best side in the history of the Premier League.

Republican senator’s comments come as he is considered among Trump’s top candidates for vice-president

The Republican Florida senator Marco Rubio said on Sunday he would not commit to accepting the 2024 presidential election results, insisting that “if it’s unfair” his party will “go to court and point out the fact that states are not following their own election laws”.

Rubio’s statements on Meet the Press come as he is considered among former president Donald Trump’s top candidates for vice-president. Trump has continuously said falsely that the 2020 election was stolen.

Taliban says four arrested over attack at Bamiyan heritage site that killed three Spanish visitors and an Afghan

Islamic State has claimed responsibility for an attack by gunmen in Afghanistan’s central Bamiyan province that killed three Spanish tourists on Friday.

The Taliban’s interior ministry spokesperson, Abdul Mateen Qani, said on Sunday that four people had been arrested over the attack. One Afghan citizen was also killed and four foreigners and three Afghans were injured in the attack, he added.

• Striker snatches Villarreal 4-4 draw and goes top of goal charts
• Slot says goodbye at Feyenoord | Montero takes charge at Juve

Alexander Sørloth struck four times in 17 minutes to help Villarreal fight back and snatch a 4-4 home draw against champions Real Madrid and take himself top of La Liga’s scoring charts.

Carlo Ancelotti’s side, crowned champions a fortnight ago, could have reached 99 points for the season, one shy of their 2011-12 record but will now fall short, as they sit on 94 before their final league game against Real Betis.

• McLaren driver pushed Max Verstappen in tense Imola climax
• Norris revealed he watched golf and boxing the night before

Lando Norris said he was praying for just one more lap to have a shot at victory at the Emilia-Romagna Grand Prix after a thrilling final fight with Max Verstappen at Imola. The British driver also revealed he had been up the night before the race until 2am, watching the title-fight boxing and the US PGA Championship golf.

Verstappen held on to win at Imola but only after the final laps came alive as Norris hunted him down, closing to within under second and ultimately finishing just 0.725sec behind the world champion. The 24-year-old McLaren driver was convinced that with another lap he would have been able to try to make a pass on Verstappen.

• Day four updates from Valhalla
• Live leaderboard | And feel free to drop Scott an email

Looking back, it should have been pretty obvious that Scottie Scheffler wasn’t going to win after the surreal incident with the peelers on Friday morning. He got back to Valhalla in time to card a jaw-droppingly dogged 66, but the mental cost must have been immense, and yesterday’s 73 was a bit of a low-energy fiasco that could have been a whole lot worse. He’s not really shifting the needle today; bogey at 1, birdie at 5, and he remains where he started at -7 through seven underwhelming holes. Time to recharge the batteries by spending some time at home with the new arrival … and OK, I’ve not quite thought that through, but you get the general gist. He’ll be back and firing on all cylinders again soon enough. Watch out Pinehurst!

It wasn’t to be for poor old Rory this week (pt XXXVIII in an ongoing series). McIlroy takes a shy at the short par-four 4th from the tee, but ends up on a grassy knoll to the side of the green. He whips out, his ball sailing through the green and over the other side, into more thick stuff, where he finds himself shortsided. But then he stabs delightfully out to three feet, such a fine mixture of power and delicacy, and scrambles his par. He remains at -7, and thoughts will already be turning to Pinehurst next month.

Exclusive: Vice-chancellors suggest fee rise of £2,000 to £3,500 a year, but others say that is ‘politically impossible’

• Next government must make hard university funding decisions, fast

Vice-chancellors and former ministers are warning that the cash crisis facing universities is so serious that the next government will have to urgently raise tuition fees or increase funding to avoid bankruptcies within two years.

They said the state of university finances was more dire than revealed in last week’s report by the Office for Students, which forecast 40% of England’s universities would end this year in the red.

Anfield said goodbye and thank you to a coach who reinvigorated the club, his impact going way beyond silverware

There was a game of football at Anfield on Sunday, and Liverpool, despite missing countless chances, as they have done consistently over the past couple of months, won it 2-0. But nobody seemed to care too much; even Gary O’Neil was restrained in his reaction to the video assistant referee intervening for Nelson Semedo’s yellow card to be upgraded to a red. It was only last week that Wolves called for the review system to be abolished: if you come at the VAR you’d best not miss.

But beneath a sky of perfect unbroken blue, this was not a day on which the game or the league table mattered; this was a day for saying goodbye, and saying thank you. “Danke Jürgen,” as the tifo running round two sides of the ground read, culminating with a heart on the Kop in the colours of the Germany flag. Liverpool knew that, whatever happened, they would finish third. That’s three places higher and, as it turned out, 20 points more than they had managed in 2014-15, the last full season before he took over, but the improvement he has wrought has been far greater than that, the outpouring of affection for him, expressed in the five-minute rendition of “I’m so glad Jürgen is a red” over the final whistle, entirely appropriate and understandable.

Le Pen, Orbán and Meloni rail against socialism and ‘massive illegal migration’ at ‘great patriotic convention’ in Madrid

International far-right leaders, including France’s Marine Le Pen, Hungary’s Viktor Orbán, Italy’s Giorgia Meloni and Argentina’s Javier Milei, came together in Madrid to rail against socialism and “massive illegal migration” three weeks before hard-right parties are expected to see a surge in support in June’s European elections.

Sunday’s “great patriotic convention”, which was organised by Spain’s far-right Vox party, offered conservatives and far-right populists a chance to congregate and take aim at a variety of familiar targets, from the welfare state to “wokeness” and the agendas of Brussels-based bureaucrats.