Suppose that 2002 numbers, each equal to 1 or -1 , are written around a circle. For every two adjacent numbers, their product is taken; it turns out that the sum of all 2002 such products is negative. Prove that the sum of the original numbers has absolute value less than or equal to 1000 . (The absolute value of x is usually denoted by |x|. It is equal to x if x \geq 0, and to -x if x<0. For example, |6|=6,|0|=0, and |-7|=7.)