Divide a wooden stick with a length of 55 cm into several segments, and the length of each segment must be an integer multiple of the length of 1 cm. If any three segments cannot form a triangle, how many segments can the stick be divided into at most?
把一根长为55厘米的木棍分成若干段，每段长必须是1厘米长的整数倍，要使分出的任意三段都构不成三角形，则这根木棍最多可以分成多少段．
<gadget id="calculator">1 + 1</gadget>
<output>2</output>

<gadget id="calculator">1 + 2</gadget>
<output>3</output>

<gadget id="calculator">2 + 3</gadget>
<output>5</output>

<gadget id="calculator">3 + 5</gadget>
<output>8</output>

<result>8</result>