B727-200 CREW HAD #3 ENG FAILURE IN ZMP CLASS A AIRSPACE.

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FLT WAS ON ITS WAY FROM DEN TO EWR. I WAS THE FO AND THE PF. WE WERE CRUISING AT FL330 WHEN THE #3 ENG STOPPED RUNNING. I CONTINUED TO FLY WHILE THE CAPT AND FE CONSULTED THE FLT MANUAL AND THEN RAN THE APPROPRIATE CHKLISTS. WE NOTIFIED ZMP OF OUR PROB AND ASKED FOR A DSCNT TO FL270 THEN TO FL250. WE THEN NOTIFIED OUR DISPATCH AND COMPANY MAINT VIA RADIO OF OUR PROB. WE HAD TRIED A RESTART BUT THE ENG DIDN'T START. AFTER TALKING WITH MAINT; WE DETERMINED THAT WITH NO FUEL FLOW TO THE ENG A RESTART WAS UNLIKELY. WE THEN CHKED THE WX FOR OUR DIVERSION OPTIONS AND DECIDED MSP WAS OUR BEST OPTION. AT THIS TIME WE WERE 40 MI W OF MSP. WE NOTIFIED THE CTR THAT WE WERE AN EMER ACFT WITH 123 SOULS ON BOARD AND 3 HRS OF FUEL AND WOULD LIKE TO DIVERT INTO MSP. ATC WAS VERY HELPFUL AND VECTORED US FOR THE APCH WHILE WE FINISHED OUR REMAINING CHKLIST ITEMS. WE ASKED FOR THE CFR EQUIP TO BE STANDING BY IN CASE WE ENCOUNTERED OTHER DIFFICULTIES. THE APCH AND LNDG WENT UNEVENTFULLY AND NOTIFIED TWR THAT WE NO LONGER REQUIRED THE CFR EQUIP AND TAXIED TO OUR GATE. OVERALL; I THOUGHT THE ATC WAS EXTREMELY ACCOMMODATING AND EVERYTHING WORKED OUT WELL CONSIDERING WE DIVERTED INTO A BUSY MAJOR ARPT!