It's Only Algebra

Algebra Level 5

\[\begin{cases}a+b-f-g=0\\
b+c-g-h=0\\
d+e-i-j=0\\
b-c+d-e-g+h-i+j=0\end{cases}\]

\(a,b,c,d,e,f,g,h,i, j\) are all numbers, each of which can only be either 0 or 1, and they satisfy the system of equations above.

Find the total number of distinct, possible values of \(a+b+c+d+e+f+g+h+i+j\).

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