The Multiply, Screen, and Overlay blend modes in image manipulation programs such as Photoshop are very useful when making digital art. If you apply one of these modes to a base colour and a top colour, a resulting colour is produced. Colours have three components: ~R~, ~G~, and ~B~, which can have any real value from ~0~ to ~1~ (completely dark to completely light) inclusive, and modes operate on each component separately. Let's call a component of the base colour ~X_a~ and the same component of the top colour ~X_b~.

If you apply the Multiply mode, the resulting component will be ~X_aX_b~. As this produces a darker colour, it is good for drawing shadows.

If you apply the Screen mode, the resulting component will be ~1 - (1 - X_a)(1 - X_b)~. As this produces a lighter colour, it is good for drawing highlights.

The Overlay mode produces different results depending on the base component. If this component is less than ~0.5~, the resulting value is ~2X_aX_b~. Otherwise, the resulting value is ~1 - 2(1 - X_a)(1 - X_b)~. As this makes dark colours darker and light colours lighter, it is good for adding contrast.

Given a blend mode and each component of the base and top colours, please find the resulting colour.

Input Specification

The first line will contain one of the following strings: Multiply, Screen, or Overlay, the blend mode.
The second line will contain 3 space-separated real numbers: ~R_a~, ~G_a~, and ~B_a~ representing each component of the base colour.
The third and final line will contain 3 space-separated real numbers: ~R_b~, ~G_b~, and ~B_b~ representing each component of the top colour.

Output Specification

Output 3 space-separated real numbers on one line: the ~R~, ~G~, and ~B~ of the resulting colour.
Your answer will be judged correct if it has an absolute or relative error less than or equal to ~10^{-6}~.

Sample Input

Multiply
0.30 0.22 0.90
0.52 0.12 0.03

Sample Output

0.156000 0.026400 0.027000