Let $N$ be positive integer. Some integers are written in a black board and those satisfy the following conditions.
1. Any numbers written are integers which are from $1$ to $N$.
2. More than one integers which is from $1$ to $N$ is written.
3. The sum of numbers written is even.
If we mark $X$ to some numbers written and mark $Y$ to all remaining numbers, then prove that we can set the sum of numbers marked $X$ are equal to that of numbers marked $Y$.
