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We give (conjectural) analogs of Berenstein-Zelevinsky data for affine type$A$. Moreover, by using these affine analogs of Berenstein-Zelevinsky data, werealize the crystal basis of the negative part of the quantized universalenveloping algebra of the (Langlands dual) Lie algebra of affine type $A$.

Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs