The robots H.E.R.P. and D.E.R.P. (don’t ask me what the acronyms stand for, because I don’t know either) are in love with each other, but they are $100$ feet away from each other. H.E.R.P. and D.E.R.P. decide to meet each other, and they give each other directions. They send out signals of their location every foot, and expect to arrive within $50$ iterations. However, due to the radio wave noise in their environment, there is a probability of $\displaystyle \frac{2}{7}$ that the signal will be incorrectly interpreted, in which case the two robots will turn $90^{\circ}$ either to the left or to the right, with equal probability. What is the expected value of iterations necessary for H.E.R.P. and D.E.R.P. will meet each other?