Consider two files systems $A$ and $B$, that use contiguous allocation and linked allocation, respectively. A file of size 100 blocks is already stored in A and also in B. Now, consider inserting a new block in the middle of the file (between $50^{\text{th}}$ and $51^{\text{st}}$ block), whose data is already available in the memory. Assume that there are enough free blocks at the end of the file and that the file control blocks are already in memory. Let the number of disk accesses required to insert a block in the middle of the file in $A$ and $B$ are $n_A$ and $n_B$, respectively, then the value of $n_A + n_B$ is ________.

1. Contiguous Allocation ($A$):

• To insert a block between the $50^{\text{th}}$ and $51^{\text{st}}$ block, the remaining 50 blocks (blocks 51 to 100) must be shifted by one position.

• Reading 50 blocks from disk: 50 disk reads.

• Writing 50 shifted blocks to disk: 50 disk writes.

• Writing the new block (at the $51^{\text{st}}$ position) to disk: 1 disk write.

2. Linked Allocation ($B$):

• To reach the $50^{\text{th}}$ block to update its pointer, traverse the linked list starting from block 1: 50 disk reads.

• Write the modified $50^{\text{th}}$ block back to disk: 1 disk write.

• Write the newly inserted block to disk (pointing to the $51^{\text{st}}$ block): 1 disk write.

Thus, the total number of disk accesses is: