GAIC Math 2024 Problem 137

There are $n$ cards, each labeled with the numbers $1 , 2, \cdots, n$. These $n$ cards are distributed among 17 people, with each person receiving at least 1 card. Then, there is always one person who receives cards with numbers $x$ and $y$, where $x>y$, and $118x \leqslant 119y$. The smallest positive integer $n$ that satisfies this condition is _____.