Balance the following equation in basic conditions

I^- +IO4^- ----> I3^- + IO3^-

Let's do it by half-reactions. But before we begin, let's recognize that the question writer is funnin' us. The real first half reaction should be: 2I- ===> I2 + 2e-. But because I2 + I- ===> I3-, we have to write:

3I- ===> I3- + 2e-

H2O +IO4- +2e- ===> IO3- + 2OH-
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H2O + 3I- + IO4- ===> I3- + IO3- + 2OH-