=+7. Consider the n-dimensional unit cube [0, 1]n. Suppose that each of its n2n−1 edges is independently assigned one of two equally likely orientations. Let S be the number of vertices at which all neighboring edges point toward the vertex. The Chen-Stein method implies that S has an approximate Poisson distribution Z with mean 1. Use the neighborhood method to verify the estimate

πS − πZTV ≤ (n + 1)2−n(1 − e−1).