Consider an array $A = [10, 7, 8, 19, 41, 35, 25, 31]$. Suppose the merge sort algorithm is executed on array $A$ to sort it in increasing order. The merge sort algorithm will carry out a total of 7 merge operations. A merge operation on sorted left array $L$ and sorted right array $R$ is said to be void if the output of the merge operation is the elements of array $L$ followed by the elements of array $R$. The number of void merge operations among these 7 merge operations is _______. (answer in integer)

Standard top-down merge sort divides the array into two halves until single-element arrays are reached, and then merges them bottom-up.

A merge of sorted arrays $L$ and $R$ produces $L$ followed by $R$ (a void merge) if and only if $\max(L) \le \min(R)$.

Let's trace the 7 merge steps for $A = [10, 7, 8, 19, 41, 35, 25, 31]$:

1. Left half $[10, 7, 8, 19]$:

   • Merge 1: $L = [10]$, $R = [7] \implies$ Output is $[7, 10]$. Not void.

   • Merge 2: $L = [8]$, $R = [19] \implies$ Output is $[8, 19]$. Since $\max(L) = 8 \le 19 = \min(R)$, output is $L$ followed by $R$. (Void #1)

   • Merge 3: $L = [7, 10]$, $R = [8, 19] \implies$ Output is $[7, 8, 10, 19]$. Not void.

2. Right half $[41, 35, 25, 31]$:

   • Merge 4: $L = [41]$, $R = [35] \implies$ Output is $[35, 41]$. Not void.

   • Merge 5: $L = [25]$, $R = [31] \implies$ Output is $[25, 31]$. Since $\max(L) = 25 \le 31 = \min(R)$, output is $L$ followed by $R$. (Void #2)

   • Merge 6: $L = [35, 41]$, $R = [25, 31] \implies$ Output is $[25, 31, 35, 41]$. Not void.

3. Final Merge:

   • Merge 7: $L = [7, 8, 10, 19]$, $R = [25, 31, 35, 41] \implies$ Output is $[7, 8, 10, 19, 25, 31, 35, 41]$. Since $\max(L) = 19 \le 25 = \min(R)$, the output is array $L$ followed by array $R$. (Void #3)

Thus, there are 3 void merge operations (Merge 2, Merge 5, and Merge 7).