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: 59 36 12 98 84 31 06 72 63

The sum of the numbers in position 3 and position 7 corresponding to step 4 is:

By analyzing the illustrative example, we can determine that the algorithm performs specific position-based swaps at each step:
* Step 1: Swap the numbers at position 3 and position 7.
* Step 2: Swap the numbers at position 1 and position 9.
* Step 3: Swap the numbers at position 4 and position 5.
* Step 4: Swap the numbers at position 3 and position 8.

Now, let's apply these exact rules to the given input sequence:
Input: 59 36 12 98 84 31 06 72 63

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

In Step 4, the number at position 3 is $72$ and the number at position 7 is $12$.

$$\text{Required Sum}=72+12=84$$