13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T630,

We call a positive integer number fair if it is divisible by each of its nonzero digits. For example, $$$102$$$ is fair (because it is divisible by $$$1$$$ and $$$2$$$), but $$$282$$$ is not, because it isn't divisible by $$$8$$$. Given a positive integer $$$n$$$. Find the minimum integer $$$x$$$, such that $$$n \leq x$$$ and $$$x$$$ is fair.

Input

The first line contains number of test cases $$$t$$$ ($$$1 \leq t \leq 10^3$$$). Each of the next $$$t$$$ lines contains an integer $$$n$$$ ($$$1 \leq n \leq 10^{18}$$$).

Output

For each of $$$t$$$ test cases print a single integer — the least fair number, which is not less than $$$n$$$.

Note

Explanations for some test cases:

In the first test case number $$$1$$$ is fair itself.
In the second test case n

Fair Numbers

Examples