12=1+1+10

12=1+2+9

12=1+3+8

12=1+4+7

12=1+5+6

12=2+2+8

12=2+3+7

12=2+4+6

12=2+5+5

12=3+3+6

12=3+4+5

12=4+4+4

Multiplying the 3 members of each partitions results in 12 **distinct** numbers: 10,18,...60,64.

On the other hand the same treatment applied to number 13 produces a pair of **equal **results: 13=1+6+6=2+2+9 and 1*6*6=2*2*9=36 (a well known problem of children's ages).

Find the smallest number which has 3 distinct partitions into 3 parts, each of them with the **same** product.

Bonus: list all numbers below 1000 boasting this feature.