K. Kalculating Damage
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Gus and Caio Fleury are two experienced Pokémon trainers. They are preparing for the next edition of the UnBalloon Pokémon League and, for that, they are running computerized battle simulations.

The simulation software they chose computes the damage of a single attack made by one Pokémon against another. To do this, it allows choosing the type of the attacking Pokémon, $$$T_a$$$, the power of the attack used, $$$P$$$, the type of the defending Pokémon, $$$T_d$$$, and the defending Pokémon's hit points, $$$H$$$. After this attack, the Pokémon's hit points are reduced to $$$max(0, H - P \cdot M(T_a, T_d))$$$, where $$$M$$$ is the type damage modifier function. If the hit points are reduced to $$$0$$$, the Pokémon is knocked out.

Gus and Caio Fleury prefer to use the most classic types: fire $$$(F)$$$, grass $$$(G)$$$, and water $$$(W)$$$. For these specific types, the function $$$M$$$ is defined as follows:

  • If $$$(T_a, T_d)$$$ $$$=$$$ $$$(F, G)$$$, $$$(G, W)$$$, or $$$(W, F)$$$, then $$$M(T_a, T_d) = 2$$$.
  • Otherwise, $$$M = \dfrac{1}{2}$$$.

Caio Fleury was using the simulator extensively to decide which strategy to use in the next battle. Meanwhile, Gus was thinking about contributing to the simulator with a custom message. Denoting by $$$X$$$ the defending Pokémon's hit points after the attack, he thought of printing "Nocaute!" if $$$X = 0$$$, and "Sobraram $$$X$$$ pontos de vida!" otherwise.

However, Caio Fleury has just challenged Gus to a battle, and now there is no time to implement this message. So now it is up to you to implement it!

Input

The first line of the input contains a single uppercase letter representing $$$T_a$$$, which can only be $$$F$$$, $$$G$$$, or $$$W$$$.

The second line also contains a single uppercase letter representing $$$T_d$$$, which can also only be $$$F$$$, $$$G$$$, or $$$W$$$.

The third line contains a single integer representing $$$P$$$ $$$(2 \leq P \leq 10^6)$$$. It is guaranteed that $$$P$$$ is even.

The fourth line also contains a single integer representing $$$H$$$ $$$(1 \leq H \leq 10^6)$$$.

Output

Print, on a single line, the message proposed by Gus, according to the statement.

Examples
Input
G
W
6
10
Output
Nocaute!
Input
G
W
4
10
Output
Sobraram 2 pontos de vida!
Input
G
G
2
2
Output
Sobraram 1 pontos de vida!