Three Racers Convergence

You are given the starting positions and speeds of three racers. The racers move in a straight line. At time t (where t is a non‐negative integer), the position of the i-th racer is given by:

\(a_i + v_i \times t\)

Your task is to determine whether there exists a time t ≥ 0 such that all three racers are at exactly the same position. Print YES if such a time exists, otherwise print NO.

Note: When all three racers have the same speed, it is assumed that they will eventually be at the same position.

inputFormat

The input consists of a single line containing six space‐separated integers:

• a₁, a₂, a₃: the starting positions of the three racers.
• v₁, v₂, v₃: the speeds of the three racers.

Mathematically, the position of the i-th racer at time \(t\) is \(a_i + v_i \times t\). All values are integers.

outputFormat

Output a single line containing either YES if the three racers will ever meet at the same position at the same time, or NO if they will not.

1 2 3 1 2 3

NO