Div divis divisible

Number Theory Level 5

Determine how many $1000$ digit numbers $A$ have the following property:

When any digit of $A$ , aside from the first, is deleted to form a $999$ digit number $B$ , then $B$ divides $A$ .

Details and assumptions

As an explicit example, the number 1000 is a 4-digit number that satisfies the above property.

The number $12=012$ is a 2-digit number, not a 3-digit number.

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