Gunnar and Emma play a lot of board games at home, so they
own many dice that are not normal $6$-sided dice. For example they own a
die that has $10$ sides
with numbers $47, 48, \ldots ,
56$ on it.
There has been a big storm in Stockholm, so Gunnar and Emma
have been stuck at home without electricity for a couple of
hours. They have finished playing all the games they have, so
they came up with a new one. Each player has 2 dice which he or
she rolls. The player with a bigger sum wins. If both sums are
the same, the game ends in a tie.
Given the description of Gunnar’s and Emma’s dice, which
player has higher chances of winning?
All of their dice have the following property: each die
contains numbers $a, a+1, \dots ,
b$, where $a$ and
$b$ are the lowest and
highest numbers respectively on the die. Each number appears
exactly on one side, so the die has $b-a+1$ sides.
The first line contains four integers $a_1, b_1, a_2, b_2$ that describe
Gunnar’s dice. Die number $i$ contains numbers $a_ i, a_ i + 1, \dots , b_ i$ on its
sides. You may assume that $1\le
a_ i \le b_ i \le 100$. You can further assume that each
die has at least four sides, so $a_ i + 3\le b_ i$.
The second line contains the description of Emma’s dice in
the same format.
Output the name of the player that has higher probability of
winning. Output “Tie” if both players have
same probability of winning.
|Sample Input 1
||Sample Output 1
1 4 1 4
1 6 1 6
|Sample Input 2
||Sample Output 2
1 8 1 8
1 10 2 5
|Sample Input 3
||Sample Output 3
2 5 2 7
1 5 2 5