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Flow is a property that is determined by the weaknesses and resistances of the types of Pokémon inside of the Purify Chamber.
In each Set, up to four Pokémon can be arranged around the Shadow Pokémon being purified. Placing a Pokémon whose type is super effective against one of the next Pokémon's types, clockwise around, will result in high flow. A type that inflicts normal damage results in weaker flow, one that is resisted will be weaker still, and one with no effect will be the weakest. Because the Normal type is not super effective against any other type, it is treated as super effective against itself in the Purify Chamber. If one has one of each of the types in each set, then the flow, in addition to the four huge bars, gets a smaller bar. If all nine sets have one of each type that is super effective against each other (i.e. Shadow Zapdos, Poliwrath, Nosepass, Flareon, and Chikorita), then the flow for each set will have a flow that fills the entire flow gauge. However, if a Pokémon is removed, then the flow for each other set will weaken by one small bar. If a Shadow Pokémon shares the same type as one of the other non-Shadow Pokémon, the flow for that Chamber will be at four, but all other Sets will have a full bar. If a Shadow Pokémon faces a Pokémon in the circle than it would be super effective against, the flow is also strengthened. Likewise, if the Shadow Pokémon faces a Pokémon it would be not very effective, or have no effect against, it will weaken the flow.
Flow is one of the most important things about the organization of Pokémon inside of the Sets. High flow among Pokémon in a group of four will raise the tempo of the music inside the chamber, causing the Shadow Pokémon in the middle to be purified very quickly, while a low flow will purify Pokémon at a rate similar to just walking around with the Pokémon in the party.
Having a high flow, and thus a high tempo, among all nine of the Sets in the Purify Chamber is the only way to purify Shadow Lugia.