March of Primality

The SMLP, an association of prime-number enthusiasts, holds its annual March of Primality to celebrate its love of prime numbers.

$N$ members will take part, each living at a distinct point on the two-dimensional plane. The route and the starting point of the march have not been fixed yet. Every participant may leave home no earlier than time $S$, and the march must reach the town's main square (the finish) no later than time $E$.

The march begins only once every participant has gathered at the chosen starting point. The organizers want to pick that starting point so that the march lasts as long as possible, that is, so that it begins as early as possible, while still reaching the finish by time $E$.

Participants (and the march itself) may follow any path; a path may wind, turn, or double back. Their maximum speed is one unit of distance per unit of time: a participant located at $(a, b)$ can, during a time interval of length $t$, move to any point whose distance from $(a, b)$ is at most $t$.

Compute the longest possible duration of the march.

The first line contains an integer $Z$ ($1 \le Z \le 10$), the number of test sets. The test sets follow.

For each test set, the first line contains three integers $N$, $S$, and $E$ ($1 \le N \le 100$; $0 \le S \le E \le 10^6$). The second line contains two integers $X_{end}$ and $Y_{end}$ ($-10^6 \le X_{end}, Y_{end} \le 10^6$), the coordinates of the finish. Each of the next $N$ lines contains two integers $x_i$ and $y_i$ ($-10^6 \le x_i, y_i < 10^6$), the coordinates of one participant's home.

For each test set, print on its own line the longest possible duration of the march, rounded to exactly one digit after the decimal point. If no march can satisfy the conditions, print the word NIE (Polish for "no") instead. Results must appear in the same order as the test sets in the input.