# Magical Numbers!

**Number Theory**Level pending

Let's define **'Magical Number'** !

A **Magical Number** **P** is a decimal number consisting of **2n** digits with the properties that

(I) No digit of **P** is **0** (Zero);

(II) Sum of the digits of **P** is equal to **A** and

(III) Product of the digits of **P** equals **B**,

where

and n is a natural number.For example, for **P**=1236 with **A**=12 and **B**=36, Sum of Digits of **P=1+2+3+6=12=A** and Product of digits of **P=1×2×3×6=36=B** . Yeah, **1236** is a Magical Number.

You have to find out the number of Magical numbers greater than 1236 and less than 1 Billion.