Consider a sequence $a$ of elements $a_0 = 1$, $a_1 = 5$, $a_2 = 7$, $a_3 = 8$, $a_4 = 9$, and $a_5 = 2$. The following operations are performed on a stack $S$ and a queue $Q$, both of which are initially empty. I: push the elements of $a$ from $a_0$ to $a_5$ in that order into $S$. II: enqueue the elements of $a$ from $a_0$ to $a_5$ in that order into $Q$. III: pop an element from $S$. IV: dequeue an element from $Q$. V: pop an element from $S$. VI: dequeue an element from $Q$. VII: dequeue an element from $Q$ and push the same element into $S$. VIII: Repeat operation VII three times. IX: pop an element from $S$. X: pop an element from $S$. The top element of $S$ after executing the above operations is ____________.

Let us trace the state of stack $S$ and queue $Q$ after each operation step-by-step:

1. Initially:

   • Stack $S = []$

   • Queue $Q = []$

2. Operation I (Push $a_0$ to $a_5$ into $S$ in order):

   • $S = [1, 5, 7, 8, 9, 2]$ (where $2$ is at the top)

3. Operation II (Enqueue $a_0$ to $a_5$ into $Q$ in order):

   • $Q = [1, 5, 7, 8, 9, 2]$ (where $1$ is at the front)

4. Operation III (Pop from $S$):

   • Pop $2$

   • $S = [1, 5, 7, 8, 9]$

5. Operation IV (Dequeue from $Q$):

   • Dequeue $1$

   • $Q = [5, 7, 8, 9, 2]$

6. Operation V (Pop from $S$):

   • Pop $9$

   • $S = [1, 5, 7, 8]$

7. Operation VI (Dequeue from $Q$):

   • Dequeue $5$

   • $Q = [7, 8, 9, 2]$

8. Operation VII (Dequeue from $Q$ and push to $S$):

   • Dequeue $7$ from $Q$ and push $7$ into $S$

   • $Q = [8, 9, 2]$

   • $S = [1, 5, 7, 8, 7]$

9. Operation VIII (Repeat operation VII three times):

   • *1st time:* Dequeue $8$, push $8$ into $S$ $\implies Q = [9, 2]$, $S = [1, 5, 7, 8, 7, 8]$

   • *2nd time:* Dequeue $9$, push $9$ into $S$ $\implies Q = [2]$, $S = [1, 5, 7, 8, 7, 8, 9]$

   • *3rd time:* Dequeue $2$, push $2$ into $S$ $\implies Q = []$, $S = [1, 5, 7, 8, 7, 8, 9, 2]$

10. Operation IX (Pop from $S$):

    • Pop $2$

    • $S = [1, 5, 7, 8, 7, 8, 9]$

11. Operation X (Pop from $S$):

    • Pop $9$

    • $S = [1, 5, 7, 8, 7, 8]$

After all operations, the top element of stack $S$ is 8.