Odd Sum equals Even sum?

If $$N$$ denote the number of $$26$$-digit numbers: $$a_1 a_2 a_3 \ldots a_{26}$$ which consists of zeros or ones only such that $$a_1 + a_3 + a_5 + \ldots + a_{23} + a_{25} = a_2 + a_4 + a_6 + \ldots + a_{24} + a_{26}$$ What is the last $$3$$ digits of $$N$$?

Details and assumptions

SInce $$N$$ is a 26-digit number, $$a_1 \neq 0$$.

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