An Insane Equation!!

Algebra Level 4

Four positive integers a,b,c,d a, b, c, d are such that

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

This problem is part of the set Hard Equations

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