National Disaster: Two Towers

Indinesia has two fire lookout towers at $(x_1, y_1)$ and $(x_2, y_2)$ with $x_1 < x_2$ and $y_1 < y_2$. Across the country there are $N$ hotspots, and the $i$-th hotspot is a circle with radius $r_i$ centered at $(fx_i, fy_i)$. A point $(x, y)$ is safe when it satisfies all of the following conditions.

1. $x_1 \le x \le x_2$,
2. $y_1 \le y \le y_2$,
3. It does not lie strictly inside any burning area. In other words, for every $1 \le i \le N$, the distance from $(x, y)$ to $(fx_i, fy_i)$ is at least $r_i$.

The locations of the two towers are guaranteed to be safe. The two towers can communicate properly if and only if there exists a safe path connecting them. A path is safe if and only if every point on it is safe. Here a path is any continuous curve, and it does not need to be straight.

Determine whether the two towers can communicate properly.

The first line contains five integers $x_1$, $y_1$, $x_2$, $y_2$ and $N$ ($-1000000 \le x_1 < x_2 \le 1000000$, $-1000000 \le y_1 < y_2 \le 1000000$, $0 \le N \le 1000$), denoting the locations $(x_1, y_1)$ and $(x_2, y_2)$ of the two towers and the number of hotspots. Each of the next $N$ lines contains three integers $fx_i$, $fy_i$ and $r_i$ ($-1000000 \le fx_i, fy_i \le 1000000$, $1 \le r_i \le 2000000$), denoting the center of the $i$-th hotspot and the radius of its burning area. No two hotspots share the same center.

Print "YES" in a line when the two towers can communicate properly, and "NO" otherwise (without quotes).

The figure below is an example of a safe path connecting the two lookout towers.

The figure below is an example of a case where no safe path exists.

The two figures below show another example of a safe path connecting the two lookout towers. The point (10, 15) in the upper figure and the point (10, 30) in the lower figure are safe.