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HILL’S DAY AT MT. CRUSHMORE

Hillary Rodham Clinton yesterday visited Mount Rushmore for a photo op beneath the stony visages of four legendary presidents – as the national Democratic Party dealt a blow to her hopes of ever joining them.

Clinton, who’s stumping hard in advance of Tuesday’s ballot in South Dakota – which will vote with Montana in the final primaries – insisted there was no deeper meaning to her choice of locale.

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“This is a tourist occasion,” she told reporters who shouted questions to her, including whether she thought she or her ex-president husband should on the South Dakota monument with George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.

As reporters called out to one of her aides to step aside and stop blocking their view of her as she gazed at the massive rock, Clinton eventually turned around. “Why don’t you go learn something about the monument?” she sniped, appearing “visibly annoyed,” according to a CBS account.

Clinton stumped as the lawyers for the Democratic National Committee delivered a setback to her campaign – and Obama predicted the party would settle on a nominee shortly after Tuesday’s contests.

“At that point, all the information will be in,” he said.

“There will be no more questions unanswered. I suspect that whatever remaining superdelegates [there are] will be able to make their decisions pretty quickly.”

Obama will be in New York headlining a fund-raiser the day after the contests.

The DNC lawyers told members of its rules committee – which meets Saturday to consider whether to seat delegates from Florida and Michigan – that no more than half of the two states’ delegates can be seated under party regulations.

That recommendation undercuts Clinton’s push for the full delegations to be included. By having the entire delegations seated, the Clinton campaign would have raised the magic number of delegates that Barack Obama needs to clinch the nomination – allowing her some room to make her case to undecided superdelegates.

But in a memo to the 30 members of the rules committee, lawyers for the DNC said the panel can “legally” restore only half the 313 pledged delegates.

Had the two states not violated party rules by moving up their primaries, Florida would have had 185 delegates and Michigan 128.

The party rules call for an automatic stripping of 50 percent of the delegates as a punishment for the calendar move.

Party lawyers said the rules committee could either seat half the delegates or seat all of them, but only have them count as half a vote each – meaning Florida and Michigan delegates would rate the same as those from territories like Guam and the Virgin Islands.

“We don’t think it’s fair to seat them fully,” said Obama campaign manager David Plouffe, whose candidate picked up three new superdelegates yesterday – meaning he needs just 45 more delegates to clinch the nomination.

Clinton booster Harold Ickes, a rules-committee member, said only the full delegations will do.

Privately, several members of the committee said they hope an agreement will be brokered by DNC Chairman Howard Dean with the two campaigns before Saturday’s meeting begins.

Allan Katz, a Tallahassee, Fla., city commissioner and committee member who backs Obama, said that any decision “has to pass the straight-face test,” and added that restoring the full delegations is “preposterous.”

Additional reporting by Charles Hurt

daphne.retter@nypost.com