Just in Time

Hello, contestant. Let us play a game. Your coach is standing in the contest room, holding a bomb that will detonate in $T$ seconds. If it goes off inside the contest room, it destroys your team's balloons and nobody else's.

The building that holds the contest room has $N$ rooms in total. Out of each room runs exactly one tunnel to a different room, and that tunnel can be used in one direction only. If room $A$ leads to room $B$, you can walk from $A$ to $B$, but you cannot walk from $B$ to $A$ unless room $B$ has a tunnel of its own to room $A$.

The bomb senses the moment your coach stops moving and detonates right then. So your coach keeps walking from room to room, and passing through one tunnel takes exactly one second. He starts in the contest room, and because each room has a single outgoing tunnel, his route is fixed by the layout of the building. The only way to save the balloons is for your coach to be somewhere other than the contest room when the bomb detonates.

You do not get the map. All I will tell you is that the tunnels were chosen uniformly at random. In exchange, you get to set $T$, which must be an integer between $2$ and $N$ inclusive. Choose $T$ so that the chance your balloons survive is as large as possible.

Exactly one value of $T$ reaches that maximum.

Let the game begin.

The first line contains one integer $N$, the number of rooms in the building ($2 \le N \le 10^9$).

Print, on one line, the value of $T$ that maximizes the probability that your balloons survive.