Batter Up

Source: Kattis

Version: Phuoc Hung OJ Extended

Problem Statement

A player has $n$ plate appearances. Each value is encoded as follows:

• 0, 1, 2, 3, 4 are the number of bases earned on an official at-bat;
• -1 is a walk, which is excluded from both the numerator and the number of official at-bats.

The slugging percentage is the sum of bases from official at-bats divided by the number of official at-bats.

Compute the player's slugging percentage.

Input

• The first line contains an integer $n$.
• The second line contains $n$ integers $a_0,a_1,\ldots,a_{n-1}$ using the encoding above.

Output

Print the slugging percentage as a real number. The answer is accepted if its absolute or relative error does not exceed $10^{-3}$.

Subtasks

Subtask 1 (100 points): $1\le n\le100$; every $a_i\in\{-1,0,1,2,3,4\}$; at least one $a_i\ne-1$.

Examples

Input

3
1 -1 4

Output

2.5

Explanation

The -1 value is a walk and is ignored. The remaining two official at-bats earn $1$ and $4$ bases, for a total of $5$ bases over $2$ official at-bats. The slugging percentage is therefore $5/2=2.5$.