a, b, and c are positive integers and satisfy the equation abc+ab+ac+bc+a+b+c+1=2004, so what is the minimum value of a+b+c?
a、b、c是正整数，并且满足等式abc+ab+ac+bc+a+b+c+1=2004，那么a+b+c的最小值是多少？
<result>171</result>