MANCHESTER, N.H. – Democrat Bernie Sanders and Republican Donald Trump rode a wave of voter frustration with American politics to commanding victories in Tuesday’s New Hampshire primaries, adding crucial credibility to their upstart candidacies.

Sanders swept majorities of men, women, independents and young people in his win over Hillary Clinton, but faces challenges in the more diverse states to come next on the primary calendar. Trump appealed to those seeking a political outsider, and he could benefit from a persistent lack of clarity among the more mainstream Republicans struggling to challenge him.

“We are going to do something so good and so fast and so strong and the world is going to respect us again, believe me,” Trump said at a victory rally.

At his own raucous rally, Sanders said his victory sent a message “that will echo from Wall Street to Washington, from Maine to California. And that is that the government of our great country belongs to all of the people and not just a handful of wealthy campaign contributors and their super PACs.”

The enthusiasm behind Trump, a real estate mogul who has never held political office, and Sanders, who says he is a democratic socialist, underscores the public’s anger with the current political and economic system. Even if neither candidate ultimately becomes his party’s nominee, whoever wins that nomination will have to reckon with the voter frustration they’ve tapped into.

Clinton appeared to recognize that reality in her concession speech, echoing Sanders’ calls for taking on Wall Street banks and tackling income inequality. But she cast herself as more prepared to make good on her pledges.

“People have every right to be angry. But they’re also hungry, they’re hungry for solutions,” she said after congratulating Sanders on his win.

New Hampshire did little to clarify the crowded contest among more mainstream GOP candidates fighting to emerge as a challenger to Trump and Texas Sen. Ted Cruz, who won the Iowa caucus. Ohio Gov. John Kasich claimed second place after devoting almost all of his campaign resources to New Hampshire, while Florida Sen. Marco Rubio and former Florida Gov. Jeb Bush battled for third, along with Cruz.

In the midst of a heated primary campaign, Kasich has prided himself on not attacking his rivals. He told supporters Tuesday night that his second-place finish could be an indication that “we’re turning the page on a dark part of American politics.”

The day was a blow for Rubio, who had appeared to be breaking away from the second-tier Republican pack after a stronger-than-expected showing in Iowa. But he stumbled in Saturday’s debate under intense pressure from New Jersey Gov. Chris Christie, who has relentlessly cast the young senator as too inexperienced and too reliant on memorized talking points to become president.

Rubio conceded that the debate may have hurt him in Tuesday’s contest and pledged to supporters that his poor performance “will never happen again.”

Christie, however, didn’t benefit from roughing up Rubio. He lagged behind the pack as votes were being tallied.

Republican voters were more negative about their politicians than Democrats, with about half of GOP voters saying they felt betrayed by party officials. Trump carried a majority of those who said they wanted an outsider to win, according to exit polls conducted by Edison Research for The Associated Press and television networks.

In a sign of Trump’s impact on the race, two-thirds of GOP voters said they supported a temporary ban on non-citizen Muslims entering the U.S., a position the billionaire outlined last year amid rising fears of terrorism emanating from the Middle East.