positive integer is the gcd of that integer with its amount of digits. Officially, gcdSum(x)=gcd(x, amount of digits of x) for a positive integer x. gcd(a,b) means the best normal divisor of an and b — the biggest integer d to such an extent that the two integers an and b are detachable by d.    For instance: gcdSum(762)=gcd(762,7+6+2)=gcd(762,15)=3.

C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter4: Selection Structures
Section: Chapter Questions
Problem 14PP
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 positive integer is the gcd of that integer with its amount of digits. Officially, gcdSum(x)=gcd(x, amount of digits of x) for a positive integer x. gcd(a,b) means the best normal divisor of an and b — the biggest integer d to such an extent that the two integers an and b are detachable by d. 

 

For instance: gcdSum(762)=gcd(762,7+6+2)=gcd(762,15)=3. 

 

Given an integer n, track down the littlest integer x≥n to such an extent that gcdSum(x)>1. 

 

Input 

 

The primary line of input contains one integer t (1≤t≤104) — the number of experiments. 

 

Then, at that point, t lines follow, each containing a solitary integer n (1≤n≤1018). 

 

All experiments in a single test are unique. 

 

Output 

 

Output t lines, where the I-th line is a solitary integer containing the response to the I-th experiment.

 

 

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