Ten people form a circle. each picks a number and tells it to the two neighbors adjacent to him in the circle. then each person computes and announces the average of the numbers of his two neighbors. the averages announced by each person (not the original number the person picked) are $1,4,9,16,25,36,49,64,81,100$ in order around the circle. find the number picked by the person who announced the average $100$.