Digit Generator, ACM/ICPC Seoul 2005, UVa1583

For a positive integer N, the digit-sum of N is defined as the sum of N itself and its digits. WhenM is the digitsumof N, we call N a generator ofM.

For example, the digit-sum of 245 is 256 (= 245 + 2 + 4 + 5). Therefore, 245 is a generator of 256.

Not surprisingly, some numbers do not have any generators and some numbers have more than one generator.For example, the generators of 216 are 198 and 207.

You are to write a program to find the smallest generator of the given integer.

Input

Your program is to read from standard input. The input consists of T test cases. The number of test casesT isgiven in the first line of the input. Each test case takes one line containing an integerN, 1 ≤ N ≤ 100,000.

Output

Your program is to write to standard output. Print exactly one line for each test case. The line is to contain agenerator ofN for each test case. If N has multiple generators, print the smallest. IfN does not have anygenerators, print 0.

The following shows sample input and output for three test cases.

Sample Input

32161212005

Output for the Sample Input

19801979

要求是根据输入的数找最小生成元,一开始我想着枚举,但量太多了。所以想着怎么去缩小搜索范围，第一想法是以万为单位，先判断出输入的数num<10000,10000<num<20000,20000<num<30000...，再想了一下明白了，条件num<100000，也就是说99999就是各个位数之和的最大和为45，所以只要从[num-45,num]这个区间搜索，就能找到想要的答案。

以下为C写的源码：