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Rutherford B. Hayes is a controversial president in the U.S. because of the disputed 1876 election, but he is a hero in Paraguay. Hayes negotiated the end of the War of the Triple Alliance, giving favorable terms to Paraguay. A department in Paraguay is named "Presidente Hayes" in his honor.
What would have happened to Paraguay if Hayes had decided not to intervene? Hayes was highly interested in Latin American affairs, so it would be difficult to arrange the right circumstances.
Paraguay already lost the majority of its population in the war, so I suppose it couldn't be much worse for them.