KöMaL 2010 B4313

$A$, $B$, $C$, $D$, $E$ and $F$ are a group of six people. $n$ bars of chocolate given to the group in the following way: Everyone gets at least one, $A$ gets less than $B$, $B$ gets less than $C$, $C$ gets less than $D$, $D$ gets less than $E$, and finally, $F$ gets the most. The members of the group know these conditions, they know the value of $n$, and of course, they know how many bars of chocolate they were given themselves. They have no other information available for them. What is the smallest possible value of $n$ for which it is possible to give them the bars of chocolate so that no one can tell how many bars of chocolate everyone has?