You have a balance with fulcrum at \((0,0)\) and pans at \(\left(\pm1,0\right)\), \(\left(\pm2,0\right)\) (as shown in the diagram). Find the least number of positive integer weights you need in order to measure any integer weight from 1 to 1000.
Note that any number of weights can be placed in any of the 4 pans (even the pan with the object you want to weigh).

Clarification: You want to be able to weigh the integer weights from 1 to 1000, but you should not assume that the object you weigh will have an integer weight.

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