Divisibility with Base 16

Let $n=11335577_{16}$ . Let $S_T$ be defined as the set of all distinct base-16 numbers that are permutations of $n$ (for example, $13135757$ , $13571357$ , $11335577$ and $77553311$ are all part of $S_T$ ). If an element in $S_T$ (let's call it $m$ ) that satisfies the condition $m-n \equiv 0 \pmod{10}$ in base ten is also in the set $S_M$ , find the last four digits of the sum of all values in $S_M$ in base ten.

For example, $13135577_{16}$ would be in $S_M$ because when both $13135577_{16}$ and $n$ are converted into base 10 ( $1 \cdot 16^7 + 3 \cdot 16^6 + \ldots + 7 \cdot 16^1 + 7 \cdot 16^0$ and $1 \cdot 16^7 + 1 \cdot 16^6 + \ldots + 7 \cdot 16^1 + 7 \cdot 16^0$ , respectively), the difference between these corresponding base-10 values is divisible by 10.