Problem B

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

Input

The first line contains number of test cases t t (1≤t≤10 3 1≤t≤10 3). Each of the next t t lines contains an integer n n (1≤n≤10 18 1≤n≤10 18).

Output

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

Example

Input

Copy

4
1
282
1234567890
1000000000000000000

Output

Copy

1
288
1234568040
1000000000000000000