ZOJ Problem Set - 2873
Yesterday, Kamran was working on a report, which he must submit to his boss next Saturday. He became tired and went out of his working room to take a nap. After some minutes, her sister, Kamelia, who is a first year university student, came to the room and found the report. She thought, "How many large positive integers in a document. I hate these large numbers, they make me see nightmares! I should represent them in a more compact way". At first, she devised an ambiguous way to represent a number. She computed the product of digits of a number to find a new number and repeated this process again and again until she reached a one digit number (For example, 972 was transformed to 126 and then to 12 and finally to 2).
But she simply understood that this process is not reversible and tried to find another way (Since she loves Kamran too much, she did not want to destroy his efforts!). Suddenly, she noticed an interesting property in all the numbers of the report and called it productivity property in her mind. By her definition, a number with productivity property is a number that can be obtained by multiplying the digits of some other number (for instance, 126, 12, and 2 has productivity property, because they can be obtained from 972, 126, and 12 respectively). She thought, "Wow, I found it. If a number x in the report is the i-th number in the increasing sequence of positive integers having productivity property, I will replace it by i". She replaced all numbers of the report, put a note for Kamran describing what she did with the numbers of his report and went to her friend��s home in a blink of an eye!!!
It is not hard to imagine, how loudly Kamran screamed when he saw the report and the note from Kamelia! In addition, he wondered how she did this! He thought "Again this naughty smart sister". Now, Kamran needs your help to find his original report numbers.
Input begins with a number T showing the number of test cases and then, T test cases follow. Each test case includes a positive integer i which is the number written by Kamran��s sister in the report. Please note than input includes thousands of test cases.
For each test case, your program must output the original number x that was converted to the given i. Please note that it is guaranteed that the output number is less than 1018.
Author: Babak Behsaz
Source: AUT Contest 1