Question 3: Consider the alignment graph based DP table below to find…

Consider the alignment graph based DP table below to find the best global alignment between two strings (represented along the rows and the columns). The DP table shown below has $n \times m$ entries i.e., $DP[0,0]$ to $DP[n,m]$, where $n$ is length of first string and $m$ is length of second string. $DP[i,j]$ is the score of best global alignment between the length-$i$ prefix of the first string and length-$j$ prefix of the second string.

Fill the DP table given below and answer the following questions accordingly.

Scoring is done as follows:

• For each match between two symbols: $+1$ point
• For each mismatch between two symbols: $0$ point
• For each removal of symbol from any one sequence: $0$ point

How many entries in the grid consists of the number 3? Enter the answer as a single integer.