Every day, Little Johnny Red picks a positive integer $m$, arbitrarily permutes the digits of $m$ to a new integer $n$, and then computes the sum $m+n$. The sums that can be produced that way are called red integers.
Every day, Little Annie Yellow picks a positive integer $p$ that entirely consists of $1$s, and then multiplies $p$ by nine. The products that can be produced that way are called yellow integers.
An integer is orange, if it simultaneoulsy belongs to the red and the yellow numbers.
Question: How many integers below one Googolplex are orange?
(Remark: All integers in this puzzle are represented in decimal, and all digits are decimal digits.)