In trapezoid A B C D with \overline{B C} \| \overline{A D}, let B C=1000 and A D=2008. Let \angle A=37^{\circ}, \angle D=53^{\circ}, and M and N be the midpoints of \overline{B C} and \overline{A D}, respectively. Find the length M N.
In trapezoid A B C D with \overline{B C} \| \overline{A D}, let B C=1000 and A D=2008. Let \angle A=37^{\circ}, \angle D=53^{\circ}, and M and N be the midpoints of \overline{B C} and \overline{A D}, respectively. Find the length M N.