The expression \sin 2^{\circ} \sin 4^{\circ} \sin 6^{\circ} \cdots \sin 90^{\circ} is equal to p \sqrt{5} / 2^{50}, where p is an integer. Find p.
The expression \sin 2^{\circ} \sin 4^{\circ} \sin 6^{\circ} \cdots \sin 90^{\circ} is equal to p \sqrt{5} / 2^{50}, where p is an integer. Find p.