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Hillary Clinton's caucus night in Iowa

It was not until Tuesday at 3:35 a.m. ET that the Clinton campaign put out a statement declaring victory. This came three hours after the Sanders campaign had issued its own statement celebrating what it called "a virtual tie," which was what CBS News also concluded in the early hours of Tuesday morning.

A Sanders campaign official complained that the Iowa Democratic Party (IDP) "failed" to staff 90 precincts, which the party dismissed as inaccurate.

The finish seemed good enough for Clinton, who wore a bright red jacket and wide smile, as she took the stage at the her Iowa caucus victory party, to one of her campaign's familiar soundtracks, Rachel Platten's "Fight Song."

"Hill-ar-y, Hill-ar-y," the crowd yelled.

With Bill and Chelsea Clinton standing behind her, Clinton shot her hands into the air like a runner crossing the finish line of a marathon. Since her first campaign visit to the state in April of 2015, it had been a long run, and this time, a better end to the caucuses than in in 200, when she lost to Barack Obama.

This time around, her campaign had worked tirelessly on the ground to turn out the vote: in the final four days of the campaign, staffers and volunteers knocked on 238,000 doors across the state.

Clinton told the crowd that she was "breathing a big sigh of relief."

"Wow, thank you so much. What a night. An unbelievable night. What a great campaign," she said with sparkling eyes.

Former Iowa Senator Harkin,who introduced her, called it a "narrow win" with Clinton gaining 22 of Iowa's delegates and Sanders claiming 21 -- but "hey, a win is a win!" he told the crowd.

A supporter decked out in red boxing gloves with Clinton stickers on them and a silky blue cape covered in stars, twirled around and punched her fists into the air exuberantly. Cell phones snapped photos.

"Yeah, yeah," the raucous crowd cheered when said to Clinton spoke about raising incomes, finishing the job of universal healthcare coverage and combatting climate change among other topics. They treated her like a winner.

Clinton did mention her competition: Sen. Bernie Sanders.

"I am excited about really getting into the debate with Senator Sanders about this best way forward to fight for America," she said. She also congratulated O'Malley for his public service. He had just dropped out of the race after attracting one percent of the vote.

Then, after about seven minutes, she left the stage and most of the crowd cleared out. Many of them hit the bar set up in another area of the building. They jubilantly toasted Clinton to "the Democratic winner of the 2016 Iowa caucus."

"I knew it was going to be a close race between Hillary and Bernie," explained 26-year old Oliver Housman, a Clinton supporter from Des Moines. "You know, I didn't think it was going to be as [close as] it was, but still very exciting."

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