\problemname{Elder price robot}
\illustration{.3}{pic}{\href{https://www.flickr.com/photos/30478819@N08/50958754723}{CC-BY 2.0, Marco Verch via Flickr}}%
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The idea behind your latest business adventure, BarGain Overview (BGO), is to collect the history of prices for a certain item that is available for sale on the web. The \emph{BarGain score} of a particular day is defined as the number of days since the price was lower or equal to today's price. The worst BarGain score is thus $1$, and if the price is strictly better than all previous prices ever recorded, then it is \texttt{infinity}. You want to report the BarGain score to your customers to help them identify a good buy.

\section*{Input}
The first line of input contains a single integer $2 \leq n \leq 400\,000$, the number of days for which you have collected price data for the item. On the second line of input follows $n$ space-separated integers $p_1, p_2, \ldots, p_{n}$, where $0 \leq p_i \leq 10^6$ is the price of the item $i-1$ days ago. Today's price is $p_1$.

\section*{Output}
Output $n$ rows, one for each day you have collected price data for the item. On the $i^{\text{th}}$ such line, output the BarGain score for the day that was $i-1$ days ago.
