It is proved that this problem belongs to the divisibility of the fifth grade Olympiad in primary school.

The difference between the last three digits and the first three digits of an integer (decreasing greatly) can be divisible by 1 1.

Let's prove that 1111...11(Yes 199 1.

First, use the first 1988 digits, namely1111...11(including1650)

Get 1111...1000 (preceded by 1985 bits1). So this topic becomes:

If 1111...11(with 1985 bits1)

Then take out the first 1982 digits, namely1111...11(with 1982

Get 1111...1000 (including 1979 bits1), ...

After repeated application for 663 times, the attribute is finally converted into: 1 1, which can be divisible by 1 1.

To sum up,1111...11(with 199 1 bit.