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.
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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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