In the following equation x, y, and n are positive integers.

1 x

+

1 y

=

1 n

For n = 4 there are exactly three distinct solutions:

1 5	+	1 20	=	1 4
1 6	+	1 12	=	1 4
1 8	+	1 8	=	1 4

What is the least value of n for which the number of distinct solutions exceeds one-thousand?

NOTE: This problem is an easier version of problem 110; it is strongly advised that you solve this one first.