Given a positive integer x, let P(x) denotes the product of all x's digits. Two integers x and y are friend numbers if P(x) = P(y). Here comes the problem: Given a positive integer x, of course it has a lot of friend numbers, find the smallest one which is greater than x.

There are multiple test cases. The first line of input is an integer T (0 < T < 230) indicating the number of test cases. Then T test cases follow. Each case is an integer x (0 < x <= 10¹⁰⁰⁰). You may assume that x has no leading zero.

For each test case, output the result integer in a single line. You should not output a number with leading zero.

The 7th Zhejiang Provincial Collegiate Programming Contest