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Fact Digit Sum
##### Submissions: 3032   Accuracy: 31.16%   Difficulty: Easy   Marks: 2

Let's define A(n) for positive integer n as a sum of factorials of its digits. For example, A(154)=1!+ 5! +4!= 145.Given a number 'x' , you need to print the minimum number L such that A(L)=x. If no such L exists, then print -1

Input:
First line contains 'T' - the number of test cases.Then each line contains an integer 'x'.

Output:
Print the answer for each value 'x'.

Constraints:
1 <= T <= 542
1000 <= x <= 109

Example:
Input:

1
40321
Output:
18

Explanations:
A(18)=1!+ 8! =40321  and 18 is the smallest element for which A(18) is 40321.
Note that A(80) = A(81) is also 40321, But among them 18 is the smallest number.

#### ** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Abhinav Jain
Author: iamabjain

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