Puzzle Time: self-referential number

[jon-nyc]

The first digit of a certain 8-digit integer N is the number of zeroes in the (ordinary, decimal) representation of N. The second digit is the number of ones; the third, the number of twos; the fourth, the number of threes; the fifth, the number of fours; the sixth, the number of fives; the seventh, the number of sixes; and, finally, the eighth is the total number of distinct digits that appear in N.

What is N?

[Klaus]

||23110105||

Another diophantine equation. The interesting question is how to get the solution analytically, without trying.