A dreadful monster has been witnessed in a forest near the city of $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ Sharia, and a group of valorous adventurers will hunt it down in few days before it hurts anyone. However, $$$\color{blue}{\text{LaLa}}$$$ knows that the real reason those adventurers are willing to take the risk is to obtain the rare $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ stone that the monster is known to produce in its intestines. $$$\color{blue}{\text{LaLa}}$$$ would like to obtain the $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ stone before they do, as it is known to be quite beautiful.
$$$\color{blue}{\text{LaLa}}$$$ will first locate the monster with her $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$. $$$\color{blue}{\text{LaLa}}$$$ has placed a bunch of $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ tools within the forest, each of which has some power associated with it.
Consider the circles centered at each $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ tool with radius equal to its power. $$$\color{blue}{\text{LaLa}}$$$'s $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ will successfully locate the monster if and only if the convex hull of the circles contains the location of the monster.
Write a program that determines whether $$$\color{blue}{\text{LaLa}}$$$ will be able to locate the monster.
The input is given in the following format:
| $$$N$$$ | ||
| $$$x_0$$$ | $$$y_0$$$ | $$$r_0$$$ |
| $$$x_1$$$ | $$$y_1$$$ | $$$r_1$$$ |
| $$$\vdots$$$ | ||
| $$$x_{N-1}$$$ | $$$y_{N-1}$$$ | $$$r_{N-1}$$$ |
where $$$N$$$ is the number of $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ tools placed in the forest, the $$$i$$$-th of which is located at $$$(x_i, y_i)$$$ and has power $$$r_i$$$. Here, assume that the forest is a two-dimensional plane where the monster is located at $$$(0, 0)$$$.
The input satisfies the following constraints:
If $$$\color{blue}{\text{LaLa}}$$$'s $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ will successfully locate the monster, print a single string "Yes". Otherwise, print a single string "No". You may print each character in either case (lower or upper).
3 -3 0 1 0 0 3 3 0 1
Yes
3 2 0 1 0 2 1 -5 -5 3
Yes
1 3 3 1
No
The following illustrates the configuration of the $$$\color{red}{\text{m}} \color{brown}{\text{a}} \color{orange}{\text{g}} \color{blue}{\text{i}} \color{magenta} {\text{c}}$$$ tools for the sample tests. The red curve denotes the boundary of the convex hull.
| First Sample | Second Sample | Third Sample |
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