KöMaL 2024 K819

Kati has written the number $+1$ ten times on the blackboard. In each move she can change the sign of five numbers on the board. She can repeat this move an arbitrary number of times. Is it possible that after a series of moves she will end up with nine $+1$'s and a single $-1$ on the board? If the answer is yes, find the minimum number of moves needed.