Consider a non-zero integer with the following properties: either a single digit, or its digits are all different and the difference between each digit except the highest digit and a digit to its left is 1 (for example, 23104), then How many numbers have the above properties? Briefly state your reasons.
考查具有如下性质的非零整数：或者是一位数，或者它的各位数字均不相同且除去最高位的数字每位数字都和其左边的某个数字之差为1(例如23104)，则有上述性质的数共有多少个．简述你的理由．
<gadget id="calculator">8 * 2</gadget>
<output>16</output>

<gadget id="calculator">1 + 16</gadget>
<output>17</output>

<gadget id="calculator">7 * 4</gadget>
<output>28</output>

<gadget id="calculator">3 + 28</gadget>
<output>31</output>

<gadget id="calculator">6 * 8</gadget>
<output>48</output>

<gadget id="calculator">7 + 48</gadget>
<output>55</output>

<gadget id="calculator">5 * 16</gadget>
<output>80</output>

<gadget id="calculator">15 + 80</gadget>
<output>95</output>

<gadget id="calculator">4 * 32</gadget>
<output>128</output>

<gadget id="calculator">31 + 128</gadget>
<output>159</output>

<gadget id="calculator">3 * 64</gadget>
<output>192</output>

<gadget id="calculator">63 + 192</gadget>
<output>255</output>

<gadget id="calculator">2 * 128</gadget>
<output>256</output>

<gadget id="calculator">127 + 256</gadget>
<output>383</output>

<gadget id="calculator">255 + 256</gadget>
<output>511</output>

<gadget id="calculator">9 + 17 + 31 + 55 + 95 + 159 + 255 + 383 + 511 + 511</gadget>
<output>2_026</output>

<result>2_026</result>