In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 2:1, and let N be the point on \overline{EH} such that HN:NE = 3:8. Line segments \overline{FH} and \overline{GM} intersect at P, and line segments \overline{FH} and \overline{GN} intersect at Q. Find \frac{PQ}{FH}.