XOR and Sum Exchange
The following holds for the 0/1 column
$ \sum_i^N x_i = K \iff \sum_i^N (1 \oplus x_i) = N - K
Even a general integer sequence can be regarded as a bit-by-bit sequence Change the order of addition ABC147D.
$ A_i = \sum_j x_{ij} 2^j
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