A997. Connecting Two Barns--Silver

Farmer John's farm consists of a set of $N$ fields $(1 \leq N \leq 10^5)$,
conveniently numbered $1 \ldots N$. Between these fields are $M$ bi-directed
paths $(0 \leq M \leq 10^5)$, each connecting a pair of fields.
The farm contains two barns, one in field 1 and the other in field $N$. Farmer
John would like to ensure that there is a way to walk between the two barns
along some series of paths. He is willing to build up to two new paths to
accomplish this goal. Due to the way the fields are situated, the cost of
building a new path between fields $i$ and $j$ is $(i-j)^2$.
Please help Farmer John determine the minimum cost needed such that barns $1$
and $N$ become reachable from each-other.

Each input test case contains $T$ sub-cases ($1\le T\le 20$), all of which
must be solved correctly to solve the input case.
The first line of input contains $T$, after which $T$ sub-test cases follow.
Each sub-test case starts with two integers, $N$ and $M$. Next, $M$ lines
follow, each one containing two integers $i$ and $j$, indicating a path
between two different fields $i$ and $j$. It is guaranteed that there is at
most one path between any two fields, and that the sum of $N+M$ over all sub-
test cases is at most $5 \cdot 10^5$.

Output $T$ lines. The $i$th line should contain a single integer giving the
minimum cost for the $i$th sub-test case.

In the first sub-test case, it is optimal to connect fields 2 and 3 with a
path, and fields 3 and 4 with a path.
In the second sub-test case, it is optimal to connect fields 3 and 4 with a
path. No second path is needed.