Yes from the Problem statement, and from a little Pen-Copy Work, you can see that, Alice is the only winner!

**Examples** :

**N=4**

**1 2 3 4**

Alice removes 2,3 then Bob removes any one of 1 & 4 then Alice removes the left peice and she wins!

**N=5**

**1 2 3 4 5**

Alice removes 2,3. Then Bob removes only 1, or both 4 and 5, Alice removes the remaining and she wins!

**N=6**

**1 2 3 4 5 6**

Alice removes 2,3, Then either Bob can remove only 1, or (4,5) or (5,6), he will only lose.

The problem meant that, **there is always a solution possible in favour of Alice, if both the players play optimally but Alice starts the Game!**

So for any N, the winner is Alice

Fastest Algorithm! O(1)