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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