Initially, $\texttt{sum = 0}$.
For $\texttt{i = 1}$,
$\texttt{j = 1}$ is skipped because $\texttt{j == i}$.
Then values added are $\texttt{1 + 2}$, $\texttt{1 + 3}$, and $\texttt{1 + 4}$.
So, $\texttt{sum = 0 + 3 + 4 + 5 = 12}$.
For $\texttt{i = 2}$,
$\texttt{j = 1}$ adds $\texttt{2 + 1 = 3}$,
$\texttt{j = 2}$ is skipped, and $\texttt{j = 3}$ adds $\texttt{2 + 3 = 5}$.
For $\texttt{j = 4}$, $\texttt{i + j = 6}$, so $\texttt{break}$ occurs.
Now, $\texttt{sum = 12 + 3 + 5 = 20}$.
For $\texttt{i = 3}$,
$\texttt{j = 1}$ adds $\texttt{3 + 1 = 4}$, and $\texttt{j = 2}$ adds $\texttt{3 + 2 = 5}$.
Then $\texttt{j = 3}$ is skipped because $\texttt{j == i}$.
For $\texttt{j = 4}$, $\texttt{i + j = 7}$, so $\texttt{break}$ occurs.
Now, $\texttt{sum = 20 + 4 + 5 = 29}$.
For $\texttt{i = 4}$,
$\texttt{j = 1}$ adds $\texttt{4 + 1 = 5}$.
For $\texttt{j = 2}$, $\texttt{i + j = 6}$, so $\texttt{break}$ occurs.
Now, $\texttt{sum = 29 + 5 = 34}$.
Therefore, the output is $\texttt{34}$.