mathematics - What is the smallest positive integer, which can not be written without repetitions of digits and using arithmetics only?

Suppose you are allowed to use all 10 digits (0,1,2,...9) at most once each; 4 arithmetic operations ($-$,$+$,$\times$,$\div$), each any number of times; parenthesises to group operations; and you can create numbers from digits by writing them together.
What is the smallest natural number which you would not be able to write?

For example, you can write:
$135 = 12*3*(9+6)/4$
and you can't write:
$11 = 11$
$3 = 2+3/3$

$27 = 3+4!$
$81 = 3^4$
$1 = 5/3$