Detect Right-Angled Triangle Among Stars

In this problem, you are given the coordinates of n stars on a 2D plane. Your task is to determine whether any three of these stars form a right-angled triangle. A triangle is right-angled if the square of one side is equal to the sum of the squares of the other two sides, i.e., it satisfies the Pythagorean theorem:

\(a^2 + b^2 = c^2\)

If such a trio of stars exists, output YES, otherwise output NO. The input will be given via standard input and the result must be printed to standard output.

inputFormat

The first line contains an integer n representing the number of stars. The following n lines each contain two integers x and y, which represent the coordinates of a star.

Example:

5
1 1
7 1
1 5
6 10
7 5

outputFormat

Output a single line with YES if there exists at least one triplet of stars that forms a right-angled triangle. Otherwise, output NO.

5
1 1
7 1
1 5
6 10
7 5

YES