Let n be an integer greater than 12. Points P_{1}, P_{2}, \ldots, P_{n}, Q in the plane are distinct. Prove that for some i, at least n / 6-1 of the distances
P_{1} P_{i}, P_{2} P_{i}, \ldots, P_{i-1} P_{i}, P_{i+1} P_{i}, \ldots, P_{n} P_{i}
are less than P_{i} Q.