HCU MCA 2014 Paper

In a convex pentagon ABCDE, the sides have lengths 1, 2, 3, 4 and 5 though not necessarily in that order. Let F, G, H, and I be the mid-points of the sides AB, BC, CD and DE respectively. Let X be the mid-point of segment FH, and Y be the mid-point of segment GI. The length of segment XY is an integer. Find all the possible values for the length of side AB. (HCU-2014)