There are 25 pieces of paper. Write a random non-zero natural number not exceeding 5 with a red pencil on the front of each piece of paper, and write a random non-zero natural number not exceeding 5 with a blue pencil on the back. The only restrictions are: On any two pieces of paper with the same red numbers, the blue numbers written must not be the same. Now multiply the red and blue integers on each piece of paper, what is the sum of these 25 products?
有25张纸片，每张纸片的正面用红色铅笔任意写上一个不超过5的非0自然数，反面用蓝色铅笔任意写上一个也是不超过5的非0自然数，唯一的限制是：红色数字相同的任何两张纸片上，所写的蓝色数字一定不能相同．现在把每张纸片上的红、蓝两个整数相乘，这25个积的和为多少．
<gadget id="calculator">1 + 2 + 3 + 4 + 5</gadget>
<output>15</output>

<gadget id="calculator">1 * 15</gadget>
<output>15</output>

<gadget id="calculator">2 * 15</gadget>
<output>30</output>

<gadget id="calculator">3 * 15</gadget>
<output>45</output>

<gadget id="calculator">4 * 15</gadget>
<output>60</output>

<gadget id="calculator">5 * 15</gadget>
<output>75</output>

<gadget id="calculator">15 + 30 + 45 + 60 + 75</gadget>
<output>225</output>

<result>225</result>