\problemname{Jinxed Betting}
Julia is betting on a large sporting competition involving matches between pairs
of teams. There are no parallel matches and each bettor receives one point for
every correct bet they make. Julia had a good streak and is in the lead.  Now she
worries that her good luck may be turning, and decides to change her strategy.

She collaborates with a betting shop owner who tells her the bets made by
everyone else. Whenever Julia makes a bet, she first checks the bets of all
bettors with the most points so far (except herself of course) and then chooses
the same team as the majority. In the case of a tie, she bets on her favourite
of the two teams in the game.

Julia wants to know for how many more
matches she is guaranteed to stay in the lead in the worst case (i.e., no
matter what bets the others make or what the outcomes of the games are).
For this problem we consider Julia to be in the lead if there is no other
bettor that has strictly more
points than her.

For example, suppose as in Sample Input 1 that Julia initially has
three points, and there are two other bettors with three and two
points respectively. For the first match, she will make the same bet
as the other bettor with three points.  If this person bets on the
losing team and the other bets on the winning team all players have an
equal score of three points.  If for the next match the other two persons bet on
different teams, Julia places the bet on her favourite, which of course
may lose.  Thus after two more matches she might lose the lead.

\section*{Input}
The input consists of:
\begin{itemize}
    \item One line with an integer $n$ ($3 \le n \le 10^5$), the
	    number of people who place their bets.
    \item One line with $n$ integers $p_1, \ldots, p_n$ ($0\le p_i \le 10^{16}$ for each $i$), the points
	    of all people who play the betting game. The first of these numbers
		corresponds to the score of Julia. You may assume that no
		other score exceeds Julia's score in the beginning.
\end{itemize}

\section*{Output}
Output the number of matches for which Julia is guaranteed to stay
in the lead.
