Defense of the Ancients (commonly known as DotA) is a custom scenario for the real-time strategy video game Warcraft III: Reign of Chaos and its expansion, Warcraft III: The Frozen Throne, based on the "Aeon of Strife" map for StarCraft. The objective of the scenario is for each team to destroy the opponents' Ancients, heavily guarded structures at opposing corners of the map. Players use powerful units known as heroes, and are assisted by allied heroes and AI-controlled fighters called "creeps". As in role-playing games, players level up their heroes and use gold to buy equipment during the mission.
Defense of the Ancients pits two teams of players against each other: the Sentinel and the Scourge. Players on the Sentinel team are based at the southwest corner of the map, and those on the Scourge team are based at the northeast corner. Each base is defended by towers and waves of units which guard the main paths leading to their base. In the center of each base is the "Ancient", a building that must be destroyed to win the game.
Each human player controls one Hero, a powerful unit with unique abilities. In DotA, players on each side choose one of 101 heroes, each with different abilities and tactical advantages over other heroes. The scenario is highly team-oriented; it is difficult for one player to carry the team to victory alone. Defense of the Ancients allows up to ten players in a five-versus-five format and an additional two slots for referees or observers, often with an equal number of players on each side.
In DotA, each hero has three basic attributes: strength, agility and intellect. One point of strength can give the hero 19 points of life and 0.03 life regen per second; One point of agility increases the hero's attack speed by 1% and every 7 points of agility increases the hero's Armor by 1; One point of intellect gives the hero 13 points of mana and 0.03 mana regen per second.
To simplify the problem, we make the following conventions: one points of strength gives a hero S points of fighting ability; one points of agility gives a hero A points of fighting ability; one points of intellect gives a hero I points of fighting ability. S, A and I are fixed but unknown real numbers. A hero with 0 points of the three attributes has 0 points of fighting ability. When two heroes fight with each other, the one has higher fighting ability always win. When two heroes that have equal fighting ability meet, one of them randomly wins.
Burning and AngleLover are both excellent DotA player. Burning is good at using the hero "Shadow Fiend" while AngleLover is famours for his "Rattletrap". They have fight with each other for n times. We knows the result and the attribute value of the two hero in each fight, but we don't know the exact value of S, A and I. Now given the attribute value of the two hero in other m fights, can you determine who will be the winer?
It is guaranteed that none of S A, and I is more than 100 times as high as another, and none of them are 0.