Recently, ufologists have discovered that flying saucers are square-shaped and, upon landing, they leave marks on the ground at the "vertices" of the saucer. You have received a secret mission: determine whether the traces left tonight were made by a flying saucer.
The input file contains four pairs of integers specifying the coordinates of the marks in the field. All coordinates are integers and do not exceed in absolute value.
Output YES if the traces were left by a UFO, otherwise output NO.
Example 1