Flying Saucers

Recently, ufologists find that flying saucers are a square, and upon landing they leave traces on the ground in the "tops" of his plate. You got a secret mission, to determine whether the traces left by tonight, traces of a flying saucer.

Input

he input file contains four pairs of numbers that specify the coordinates of the marks on the field. All coordinates are integers and do not exceed the modulo 32767.

Output

The output file you want to display YES if the tracks by UFO, otherwise the output NO.

Examples