Lich Sandro is standing on the floor of a triangular pyramid at the point (x₀, y₀, 0). The vertices of the pyramid have coordinates (x₁, y₁, 0), (x₂, y₂, 0), (x₃, y₃, 0), (x₄, y₄, H). He wants to fly to the point (x₀, y₀, h) and create a spherical force field centered at that point. A rise to the height z takes z units of mana. Creating a field of radius r takes r units of mana. If the force field has at least one common point with the walls or floor, then the pyramid collapses. Initially Sandro has m units of mana. Is this amount sufficient to break the pyramid with a force field?

The first line contains the integers m, h, H (1 ≤ m, h, H ≤ 1000). In the following five lines, you are given the integers x_i, y_i, where 0 ≤ i ≤ 4 (−1000 ≤ x_i, y_i ≤ 1000). The point (x₀, y₀, h) lies strictly inside the pyramid.

Output “YES” if Sandro can break the pyramid with a force field, otherwise output “NO”.