Three Safe Treasure Collection

Charlotte is on a quest to collect exactly three treasures. Each treasure is guarded by a magnetic field that forms a circle with a given center \((x, y)\) and radius \(r\). The magnetic fields of the treasures must not overlap; formally, for any two selected treasures with centers \((x_1, y_1)\) and \((x_2, y_2)\) and radii \(r_1\) and \(r_2\), the fields are considered separate if

[ (x_1 - x_2)^2 + (y_1 - y_2)^2 \ge (r_1 + r_2)^2 ]

Your task is to determine whether there exists a set of three treasures satisfying the above condition. If such a combination exists, print the coordinates (formatted as (x, y)) of each treasure in lexicographical order. Otherwise, output the message "Charlotte cannot collect three treasures."

inputFormat

The input is read from standard input (stdin) and is formatted as follows:

• The first line contains an integer \(n\) representing the number of treasures.
• The next \(n\) lines each contain three integers \(x\), \(y\), and \(r\) separated by spaces, where \((x, y)\) is the coordinate of a treasure and \(r\) is the radius of its magnetic field.

outputFormat

Output is written to standard output (stdout). If there exists a valid combination, print three lines, each line showing the coordinate of a treasure in the format (x, y). If no valid combination exists, print a single line with the text "Charlotte cannot collect three treasures."

## sample

5
100 100 50
800 800 40
1500 1500 60
300 300 30
1200 1200 50

(100, 100)
(300, 300)
(800, 800)

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