A memory is provided with a plurality of column groups and two redundant column groups. If there are two defective columns in the plurality of column groups, the plurality of column groups may be divided into a no-shift region, a one-shift region, and a two-shift region. The memory includes a plurality of input/output circuits corresponding to the plurality of column groups. Each input/output circuit may provide a data input signal during a write operation and receive a data output signal during a read operation. Each input/output circuit also includes a switch matrix. In the no-shift region, the switch matrix couples the input/output circuit to a core in the corresponding column group. In the one-shift region, the switch matrix couples the input/output circuit to a core in a subsequent column group. In the two-shift region, the switch matrix couples the input/output circuit to a core in a next-to-subsequent column group.