Batter Up

While the Chicago Cubs were ecstatic with their 2016 World Series championship, they were eliminated from the playoffs in 2017. Looking ahead to 2018 they are beginning to embrace the more data-driven analysis of player’s values known as Sabermetrics.

For example, a player’s batting average is calculated by
dividing the total number of base hits by the total number of
official at-bats. One limitation of using the batting average
to evaluate players is that it treats all hits equally, rather
than taking into account doubles, triples or home runs. For
this reason, analysts often prefer to consider what is known as
the *slugging percentage*, which distinguishes between
different hit outcomes. To calculate the slugging percentage,
the total number of *bases* of all hits is divided by
the total numbers of time at bat, that did not result in walks,
or *at-bats*.

More specifically, an at-bat can earn $0$, $1$, $2$, $3$ or $4$ bases (these are referred to as
*official* at-bats). Furthermore, some at-bats, such as
those that result in a base-on-balls (i.e., a “walk”) are not
considered in either the player’s batting average or slugging
percentage.

For example, if a player hits a triple ($3$ bases), strikes out ($0$ bases), and hits a double ($2$ bases), their slugging percentage would be $\frac{3+0+2}{3} \approx 1.6667$. If a player hits a single ($1$ base), walks, and hits a home run ($4$ bases), the slugging level would be $\frac{1 + 4}{2}=2.5$. Notice that in this case, the denominator is two, not three, because the walk does not count towards the slugging percentage.

The input is composed of two lines. The first line contains
a single positive integer $n$ ($1
\le n \le 100$) that specifies the number of at-bats.
The second line contains $n$ integers, separated by spaces,
each describing one of those at-bats. Strike-outs, singles,
doubles, triples, and home runs are represented as `0`, `1`, `2`, `3`, `4`, respectively. Walks are represented as
`-1`. You may assume that there will
always be at least one official at-bat (i.e., at least one
at-bat will *not* be a walk).

Display the player’s slugging percentage as a real number,
accurate to within an absolute or relative error of
$10^{-3}$. We recommend
that you do *not* round the value that you
calculate.

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

3 3 0 2 |
1.6666666666666667 |

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

3 1 -1 4 |
2.5 |

Sample Input 3 | Sample Output 3 |
---|---|

11 -1 -1 -1 -1 0 0 0 0 0 0 1 |
0.14285714285714285 |