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  Wales have qualified as Group B winners thanks to their 3-0 win over Russia which is being described as arguably their greatest ever performance.
  They will play either Northern Ireland, Turkey or Albania in Paris on Saturday.
  "Now that we've qualified we want to see where we can go, and anything can happen now in these games. We are trying to get through," Ramsey said.
  "Our main target was to get out of the group, and to finish top of the group is a fantastic feeling. It means so much. I think we've made the fans proud."
  Ramsey's superb display against Russia saw him win the Uefa man of the match award, scoring the first goal before Neil Taylor and Gareth Bale added gloss to a glorious night for Welsh football.
  Wales are playing in a first major tournament for the first time since the 1958 World Cup.
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  Defender James Chester says Wales will test anyone at Euro 2016 if they reproduce the form that saw them clinch top spot in Group B.
  "If we perform like we did against Russia and keep clean sheets, which is another bonus, then we're confident that we can make it difficult for anybody," he said.
  "The way we dug in for the game and to lose so late on against England was a big kick in the stomach.
  "But we knew that result wouldn't define the group.
  "I said after the England game from what we'd seen of Russia I was confident we could get something from the game and that proved to be correct."
  Wales captain Ashley Williams agreed with the sentiment.
  "Whoever we get we're not too fussy, you just have to play whoever's put in front of you and we've played three very good teams so far in this tournament, so whoever it is we'll prepare for them," he told BBC Radio Wales Sport.
  "I'm sure the Welsh fans will come again in their numbers and make a lot of noise. We're just happy we got on top of the group. Whoever we get, we will try and progress as much as we can."
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  Chester says Wales owe a debt to the efforts of Bale.
  The world's most expensive player scored seven times in 10 qualifiers and now has three in the tournament itself.
  Bale's goal against Russia took him to joint fourth on Wales' all-time scoring list with 22, six behind record goalscorer Ian Rush.
  "I'm not sure there's a better player individually than Gareth in the tournament," said Chester.
  "We know how fortunate we are to have him in our team and if we can keep clean sheets then we know we give ourselves a real good chance.
  "I can't speak for any of the other top players in the tournament - I don't know them - but Gareth is very passionate about playing for the national team.
  "He turns up pretty much every time we have a game, which some of the top players maybe don't do.
  "I think it's an environment that he really enjoys and we all get on really well together.
  "As big a superstar as he is, he's still one of the lads."
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target: Aaron Ramsey and his Wales team-mates say they are not worried about who they might face in the last 16 at Euro 2016.