An Insane Equation!!

Algebra Level 4

Four positive integers \( a, b, c, d \) are such that

\( abcd+abc+bcd+cda+dab\\+ab+bc+cd+da+ac+bd+a+b+c+d = 2009 .\)

What is the value of \( a+b+c+d \)??

This problem is part of the set Hard Equations

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