Lunch Break

Super spy Lance Sterling is in the city and is about to leave for a mission. For convenience, a rectangular coordinate system is set up over the city, where the unit segment is one meter long. Lance is currently in a secret hideout at $(x_s, y_s)$ and needs to reach $(x_t, y_t)$. He can move in any direction at a speed of 1 meter per second. He is very hungry, though, so he decided to grab a bite before the mission.

The city has $n$ restaurants where Lance can eat. Restaurant $i$ is at $(x_i, y_i)$, and Lance spends exactly $t_i$ seconds eating there. Find the minimum time needed to reach the destination if he stops at one of the restaurants on the way.

The first line contains four integers $x_s$, $y_s$, $x_t$, and $y_t$, the coordinates of the hideout and the destination ($|x_s|, |y_s|, |x_t|, |y_t| \le 1\,000$).

The second line contains one integer $n$, the number of restaurants ($1 \le n \le 1\,000$).

Each of the next $n$ lines contains three integers $x_i$, $y_i$, and $t_i$, the coordinates of restaurant $i$ and the number of seconds spent eating there ($|x_i|, |y_i| \le 1\,000$, $1 \le t_i \le 1\,000$).

Print one real number, the minimum number of seconds Lance needs to reach the destination after stopping at a restaurant. The answer is accepted if its absolute or relative error does not exceed $10^{-9}$.