It is known that the product of n natural numbers is 2007, and the sum of these n natural numbers is also 2007, so what is the maximum value of n?
已知n个自然数之积是2007，这n个自然数之和也是2007，那么n的值最大是多少．
<gadget id="calculator">3 + 3 + 223</gadget>
<output>229</output>

<gadget id="calculator">2_007 - 229</gadget>
<output>1_778</output>

<gadget id="calculator">1_778 + 3</gadget>
<output>1_781</output>

<result>1_781</result>