Morse code is a classical way to communicate over long distances, but there are some drawbacks that increase the transmission time of long messages.
In Morse code, each character in the alphabet is assigned a sequence of dots and dashes such that no sequence is a prefix of another. To transmit a string of characters, the sequences corresponding to each character are sent in order. A dash takes twice as long to transmit as a dot.
Your alphabet has $$$n$$$ characters, where the $$$i$$$-th character appears with frequency $$$f_i$$$ in your language. Your task is to design a Morse code encoding scheme, assigning a sequence of dots and dashes to each character, that minimizes the expected transmission time for a single character. In other words, you want to minimize $$$f_1t_1 + f_2t_2 + \cdots + f_nt_n$$$, where $$$t_i$$$ is the time required to transmit the sequence of dots and dashes assigned to the $$$i$$$-th character.
The first line contains an integer $$$n$$$ ($$$2\le n\le 200$$$) — the number of characters in the alphabet.
The second line contains $$$n$$$ real numbers $$$f_1$$$, $$$f_2$$$, $$$\ldots$$$, $$$f_n$$$ ($$$0 < f_i < 1$$$) — $$$f_i$$$ is the frequency of the $$$i$$$-th character. All values $$$f_1$$$, $$$f_2$$$, $$$\ldots$$$, $$$f_n$$$ are given with exactly four digits after the decimal point. The sum of all frequencies is exactly 1.
Print $$$n$$$ lines, each containing one string consisting of dots $$$\texttt{.}$$$ and dashes $$$\texttt{-}$$$. The $$$i$$$-th line corresponds to the sequence of dots and dashes that you assign to the $$$i$$$-th character.
If there are multiple valid assignments with the minimum possible expected transmission time, any of them is considered correct.
30.3000 0.6000 0.1000
-. . --
30.3000 0.4500 0.2500
.. - .-
In the first sample, the alphabet contains three letters, say $$$a$$$, $$$b$$$, and $$$c$$$, with respective frequencies $$$0.3$$$, $$$0.6$$$, and $$$0.1$$$. In the optimal assignment, we assign $$$a$$$ to '$$$\texttt{-.}$$$', $$$b$$$ to '$$$\texttt{.}$$$', and $$$c$$$ to '$$$\texttt{--}$$$'. This gives an expected transmission time of $$$0.3 \cdot 3 + 0.6 \cdot 1 + 0.1 \cdot 4 = 1.9$$$ time units per character, which is optimal.
For comparison, the assignment $$$a\to$$$ '$$$\texttt{..}$$$', $$$b \to$$$ '$$$\texttt{-}$$$', $$$c \to$$$ '$$$\texttt{.-}$$$' has an expected transmission time of $$$0.3 \cdot 2 + 0.6 \cdot 2 + 0.1 \cdot 3 = 2.1$$$. The assignment $$$a \to$$$ '$$$\texttt{-}$$$', $$$b \to$$$ '$$$\texttt{.}$$$', $$$c \to$$$ '$$$\texttt{..}$$$' has a lower expected transmission time, but is invalid since '$$$\texttt{.}$$$' is a prefix of '$$$\texttt{..}$$$'.
