Okay, where does it end?

Algebra Level 4

$\large\displaystyle Y= \left[ \left(1+\frac{1}{n}\right) \left(1+\frac{2}{n}\right) \left(1+\frac{3}{n}\right) \cdots \left(1+\frac{n}{n}\right) \right]^{\frac{1}{n}}$

Find the value of $\lceil Y \rceil$ , where $n$ is a positive integer.

Submit your answer as 123 if you think that the answer depends on the value of $n$

Notation: $\lceil \cdot \rceil$ denotes the ceiling function.

This problem is a part of the set All-Zebra