On a circular board, there are $19$ squares numbered in order from $1$ to $19$. To the right of $1$ is $2$, to the right of $2$ is $3$, and so on, until $1$ is to the right of $19$. In each box, there is a token. Every minute, each token moves to its right by the number of the box it is in at that moment plus one. For example, the token that is in the $7$th place moves the first minute $7 + 1$ places to its right to the $15$th square. The second minute, that same token moves $15 + 1$ places to the right, reaching square $12$, and so on. Determine if, at some point, all the tokens return to the place where they started, and if so, how many minutes must elapse.

Let's think step by step and output the final answer within \boxed{}.
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