ZDC CTLR EXPERIENCED OPERROR AT FL360; FAILING TO NOTE CONFLICTING TFC IMMEDIATELY AFTER HURRIED RELIEF BRIEFING DUE TO STAFFING LIMITATIONS.

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THE INITIAL PROB ALL STARTED WHEN WE ONLY HAD 5 PEOPLE THAT NIGHT TO STAFF A 6 SECTOR AREA. THE SUPVR; DUE TO STAFFING; COMBINED SEVERAL SECTORS JUST SO WE COULD OPERATE WITH 1 PERSON ON BREAK. EACH PERSON HAD TO DO 2 HRS 30 MINS (AT LEAST) EACH ROTATION. ONE OF MY CO-WORKERS; WHO WAS ON THE SECTOR FOR CLOSE TO 3 HRS; NEEDED TO USE THE BATHROOM. I WAS INSTRUCTED TO LEAVE THE RADAR ASSISTANT POS ON ANOTHER SECTOR TO RELIEVE HIM SO HE COULD GO TO THE BATHROOM. JUST PRIOR TO HIM GIVING ME A VERY SHORT RELIEF BRIEFING; HE ISSUED A DSCNT CLRNC TO AN ACFT. NEITHER OF US NOTICED THAT THE CLRNC HE JUST ISSUED PUT HIM IN CONFLICT WITH ANOTHER ACFT. 1 MIN 12 SECONDS LATER; AFTER I SIGNED ON THE POS; THE CONFLICT ALERT WENT OFF AND I TOOK IMMEDIATE ACTION TO SOLVE THE CONFLICT. IT WAS TOO LATE AND THERE WAS A LOSS OF SEPARATION; SO AFTER I JUST HAD THE OPERROR; DUE TO STAFFING; I COULD NOT BE RELIEVED OF POS -- I HAD TO CONTINUE TO WORK TFC FOR ANOTHER 1 1/2 HRS BEFORE GETTING A BREAK. MGMNT IS SUPPOSED TO GET THE INDIVIDUAL OFF POS AFTER YOU ARE INVOLVED. IT WAS VERY DIFFICULT TO CONCENTRATE AFTER JUST MOVING 2 AIRPLANES GET TOO CLOSE TO ONE ANOTHER. AND BEING FORCED TO CONTINUE TO WORK TFC FOR SUCH A LONG TIME AFTER THE OCCURRENCE DIDN'T HELP THE STRESS OR ANXIETY.