Fast Writing, the Duel
By Gustavo Policarpo, INATEL 
Brazil
By Gustavo Policarpo, INATEL Brazil
Matheus and his twin brother Vinicius love to fight to see who is typing the fastest. After many years of mourning, they came to the conclusion that the duel is not always won by the one who only types faster, as other factors influence the winner. As each participates in their own home, they have a certain delay to receive and send data from the server. They also have a different reaction time, which can cause some of them to type in later. And of course, each one has its typing speed.
Given the delay regarding the connection of each one, its reaction time, and the speed of writing, who will be the winner?
The input consists of 3 lines. In the first one will be provided three integers Am, Rm, Em, representing respectively the delay time of the Matheus connection, its reaction time and the writing time, that is, the time it takes to type each character regardless of which one , in milliseconds. In the second line will be provided three integers Av, Rv, Ev, with the information of Vinicius. The third and last line consists of a S phrase, containing only alphanumeric characters, punctuation marks and spaces used in the duel.
1 ≤ Am, Rm, Em, Av, Rv, Ev ≤ 1000
1 ≤ | S | ≤ 100000
You must inform who will be the winner of the duel, or "Empate" without the quotes if it ends tied.
| Input Samples | Output Samples |
|
5 3 1 1 1 2 esta Matheus vence |
Matheus |
|
10 5 1 1 1 2 agora Vinicius ganha |
Vinicius |
|
5 3 1 3 7 1 Empate!!! |
Empate |