298. Dice Game

Problem Statement:
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, . . . , 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, . . . , 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.

Input Format:
The first line contains four integers a1, b1, a2, b2 that describe Gunnar's dice. Die number i contains numbers ai, ai + 1, . . . , bi on its sides. You may assume that 1 ≤ ai ≤ bi ≤ 100. You can further assume that each die has at least four sides, so ai + 3 ≤ bi. The second line contains the description of Emma's dice in the same format.

Output 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 4 1 4 1 6 1 6 1 8 1 8 1 10 2 5 2 5 2 7 1 5 2 5

Sample Output:
Emma Tie Gunnar

 Added by: hossamyosef Added at: 2014-10-21 17:00:00 UTC Time Limit: 3 seconds Partial score: No Source: Nordic Collegiate Programming Contest