Gondola sequence check

The Maokong gondola in Taipei runs on a circular track with one station. Initially gondolas $1$ through $n$ sit in order, all moving the same way. After gondola $i$ passes the station, gondola $i+1$ passes next (after $n$ comes $1$).

Gondolas can break. Spare units are numbered $n+1, n+2, \ldots$ and the smallest unused spare replaces a broken gondola in the same slot. With $n=5$, if gondola $1$ breaks it becomes gondola $6$.

Write down the numbers of $n$ consecutive passings at the station in order to form a gondola sequence. Some breaks may already have happened before you start writing, but no gondola breaks while you write.

The same physical layout can yield different sequences depending on when you start. With no breaks, $(2,3,4,5,1)$ and $(4,5,1,2,3)$ are valid but $(4,3,2,5,1)$ is not.

If only gondola $1$ broke, $(4,5,6,2,3)$ is possible. If gondola $4$ then breaks and becomes $7$, $(6,2,3,7,5)$ works. If $7$ later breaks and becomes $8$, $(3,8,5,6,2)$ is also possible.

The replacement sequence lists broken gondolas in break order; here it is $(1,4,7)$.

Decide whether the input sequence could appear after some replacement history.

The first line contains $n$.

The second line contains $n$ integers.

Print $1$ if the sequence is possible, otherwise $0$.

Keep the next-gondola map on the circle. For each original id $1..n$ missing from the sequence, replace it with the next spare id, chaining further replacements when a spare is also absent. Finally verify every consecutive pair in the input follows the successor links.