Add a positive sign and a negative sign arbitrarily in front of 1, 2, 3..., 2009, what is the smallest non-negative number that can be obtained by their algebraic sum?
在1，2，3…，2009前面任意添上一个正号和负号，它们的代数和，可以得到最小的非负数是多少？
<gadget id="calculator">1_004 + 1_007</gadget>
<output>2_011</output>

<gadget id="calculator">1_005 + 1_006</gadget>
<output>2_011</output>

<gadget id="calculator">2_011 - 2_011</gadget>
<output>0</output>

<gadget id="calculator">1 + 0</gadget>
<output>1</output>

<result>1</result>