Direction: Study the following information carefully and answer the questions given below.
An algorithm rearranges a sequence of numbers following a specific rule in each step. Following is an illustration of input and the subsequent steps of rearrangement.

Input: 98 31 06 72 63 59 36 12 84
Step 1: 98 31 36 72 63 59 06 12 84
Step 2: 84 31 36 72 63 59 06 12 98
Step 3: 84 31 36 63 72 59 06 12 98
Step 4: 84 31 12 63 72 59 06 36 98

Input: 12 31 59 36 63 72 98 84 06

The sum of the numbers for the given sequence whose positions remain unaltered through all the steps as in the input is:

The rearrangement algorithm executes fixed position-based swaps at each step:
* Step 1: Swap position 3 and position 7
* Step 2: Swap position 1 and position 9
* Step 3: Swap position 4 and position 5
* Step 4: Swap position 3 and position 8

Let's apply these steps to the new input sequence:
Input: 12 31 59 36 63 72 98 84 06

* Step 1 (Swap 3 & 7): 12 31 98 36 63 72 59 84 06
* Step 2 (Swap 1 & 9): 06 31 98 36 63 72 59 84 12
* Step 3 (Swap 4 & 5): 06 31 98 63 36 72 59 84 12
* Step 4 (Swap 3 & 8): 06 31 84 63 36 72 59 98 12

Now, track the values across all operations to find which positions never change relative to the initial input:

* Position 2 contains the number $31$ and stays unaltered through all steps.
* Position 6 contains the number $72$ and stays unaltered through all steps.

Sum of these unaltered values:

$$\text{Sum}=31+72=103$$