Choose 3 pairs of different positive integers from 1, 2, 3...100 so that their sum can be divisible by 3. How many ways are there to choose?
从1，2，3…100中选取3个两两不同的正整数，使得它们的和能被3整除，问有多少种选取方法？
<gadget id="calculator">34 * 33 * 32</gadget>
<output>35_904</output>

<gadget id="calculator">3 * 2 * 1</gadget>
<output>6</output>

<gadget id="calculator">35_904 / 6</gadget>
<output>5_984</output>

<gadget id="calculator">33 * 32 * 31</gadget>
<output>32_736</output>

<gadget id="calculator">32_736 / 6</gadget>
<output>5_456</output>

<gadget id="calculator">35_904 + 5_984 + 5_456 + 5_456</gadget>
<output>52_800</output>

<result>52_800</result>