Lars Lagerback is a bit concerned about the state of affairs in Iceland when the country's football team, which he co-coaches, take on England on Monday in the last 16 of Euro 2016.

"I hope that someone keeps the country going," the Swedish trainer quipped, after Iceland set up the England date in Nice with a last-gasp 2-1 win over Austria on Wednesday.

Some 10,000 fans were on hand at the Stade de France, an astonishing number given Iceland's population of 300,000, which makes it the smallest country to ever compete at the Euros.

Iceland made headlines by qualifying from a tough group in which they beat the Netherlands twice. It got even better in France, where they first drew 1-1 with Cristiano Ronaldo's Portugal, then had to swallow a late 1-1 equalizer against Hungary before beating Austria on the last play of the match from Arnor Ingvi Traustason.

Incredible scenes followed as all players and staff piled on the scorer, and then everyone went over to celebrate with the fans.

"It's amazing, and of course with all these supporters, 10,000 fans from Iceland is incredible. It is like a family. I know 50 per cent of the crowd or recognize them. This is extra sweet for us," man-of-the-match Kari Arnason said.

Captain Aron Gunnarsson spoke of his "greatest day" in football: "You probably only experience this once in your career."

The other coach, Heimir Hallgrimsson, said: "I guess we will change the national holiday, which normally on June 17, by a few days. That is what this means to us."

Ronaldo had dismissed Iceland as "small minded" and defensive after their draw. After Iceland reached the last 16 - ahead of Portugal from their group - Hallgrimsson was dismissive.

"What he says is irrelevant for us. We don't mind what other people think of us," Hallgrimsson said.

A mighty team and fighting spirit, firm defence and dangerous counter-attacking have been the keys to success for Iceland, who are aware of their limitations on the pitch.

"A fighting spirit and hard work - that's our philosophy," Gunnarsson said.

Hellgrimsson added: "The others have better individual skills, but we leave it all on the pitch."

Looking at Wednesday's match, where Jon Dadi Bodvarsson opened the scoring, and Alessandro Schoepf levelled for Austria, whose Aleksadar Dragovic missed a penalty, Hellgrimsson said: "We sacrificed everything for the win. We were lucky at occasions, but we showed fantastic mentality."

The reward is the date with England, which is as good as it gets for the team.

"We are all English football crazy. We don't have to analyse them much," Hellgrimsson said. "There is a lot of talent in the England team. ... I am not afraid of the England match. The players know how much fun it is to win."

Arnason said he normally supports England: "But I am buzzing to meet them. ... It is a dream come true. We will go into game with full force, to get a result. We believe in our ability."

They know that this could well be the end of the journey, even though Lagerback pointed out he never lost against England during his past term as Sweden coach.

"Everyboby knows Iceland has to have the perfect game, the best game. We know that. We can still lose against a team like England, that's a fact," Hellgrimsson said.

But there is always the undying support from the fans to count on, including a fearful chant, which reminded one journalist of a Viking chant when he quizzed Hellgrimsson about its origin.

"It's a chant from one of our clubs, which the fans stole," Hellgrimsson said. "If you are afraid, we will keep on doing it."

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