# Problem C

Taktsveðjur

Languages
en
is
Atli plays video games instead of being productive embarrassingly often. Often people are trying to reach him but can’t due to him being in virtual reality and hearing nothing. Almost without fail he is playing his favourite game Taktsveðjur when he is in virtual reality. Taktsveðjur revolves around swinging swords and trying to hit all the notes that appear, often to the rhythm of some good music. A lot of effort goes towards getting as high a score as possible for a given song and beating high scores. Since Atli is too busy swinging his arms around and beating high scores, someone else has to take care of adding up the score!

In Taktsveðjur you get points for each note hit. Each note is worth between $1$ and $115$ points, if you fail to hit the note you get $0$ points. On top of this there is a score multiplier that is determined by how many notes you hit in a row. At the start the multiplier is $1$, so the note gives you as many points as it is worth. If you hit two notes in a row the multiplier goes to $2$ and you get twice as many points as the notes are worth. If the multiplier is $2$ and you hit $4$ notes in a row the multiplier goes to $4$. Similarly if it is $4$ and you hit $8$ notes in a row the multiplier goes to $8$, which is the highest possible multiplier. If a note gets you to a new multiplier the new multiplier is applied to that note. For example if you hit the first two notes of a song you already get double points for the second one. If you miss a note the multiplier lowers by one step, going from $8$ to $4$, $4$ to $2$ or $2$ to $1$. If the multiplier is $1$ it stays at $1$ if you miss a note.

## Input

The first line of input contains a single integer $n$, the number of notes in the song Atli played. Next there are $n$ lines, each containing the score for one note in the song. Each line therefore contains a single integer $x$ satisfying $0 \leq x \leq 115$.

## Output

Print the total score Atli gets for the song.

## Scoring

Group |
Points |
Constraints |

1 |
20 |
$1 \leq n \leq 100$, Atli hits no notes. |

2 |
20 |
$1 \leq n \leq 100$, Atli never hits two or more notes in a row. |

3 |
20 |
$1 \leq n \leq 100$, Atli misses no notes. |

4 |
20 |
$1 \leq n \leq 100$. |

5 |
20 |
$1 \leq n \leq 100\, 000$. |

Sample Input 1 | Sample Output 1 |
---|---|

4 100 100 0 100 |
400 |

Sample Input 2 | Sample Output 2 |
---|---|

17 100 100 100 100 100 100 100 100 100 100 100 100 100 100 0 0 115 |
5130 |