The vacation started, and Lutfi asked his friend to give him a list of movies to watch during his vacation.

Lutfi's friend has a list with $n$ movie ratings, the $i^{th}$ movie has a rating $a_i$

Lutfi is going to choose two indices $i$ and $j$, such that $i \leq j$ and $j \leq n$, and watch the movies with ratings $a_i, a_{i + 1}, a_{i + 2}, ..., a_j$.

After he finishes watching the movies, Lutfi's happiness will be equal to the sum of the ratings of the movies that he chose to watch. Your task is to find the maximum happiness that Lutfi can achieve, assuming that he chooses $i$ and $j$ optimally.

Of course, Lutfi will watch at least one movie so his friend doesn't get mad at him.