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 $X_a{X}_b$. 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 $2X_a{X}_b$. 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