Codeforces875A-Classroom Watch

Classroom Watch

Eighth-grader Vova is on duty today in the class. After classes, he went into the office to wash the board, and found on it the number n. He asked what is this number and the teacher of mathematics Inna Petrovna answered Vova that n is the answer to the arithmetic task for first-graders. In the textbook, a certain positive integer x was given. The task was to add x to the sum of the digits of the number x written in decimal numeral system.

Since the number n on the board was small, Vova quickly guessed which x could be in the textbook. Now he wants to get a program which will search for arbitrary values of the number n for all suitable values of x or determine that such x does not exist. Write such a program for Vova.

Input

The first line contains integer n (1 ≤ n ≤ 10⁹).

Output

In the first line print one integer k — number of different values of x satisfying the condition.

In next k lines print these values in ascending order.

Example

Input

21

Output

115

Input

20

Output

0

Note

In the first test case x = 15 there is only one variant: 15 + 1 + 5 = 21.

In the second test case there are no such x.

题意：定义函数：f(x) = x + 十进制下x各位上的数字之和。给你f(x)的值（f(x) <= 1e9），让你输出所有可能的x值。题解：第三题似乎也很简单。我们直接从n-120到n枚举答案就可以了。

Code：

var n,i,x,ans,k:longint;q:array[0..1000]of longint;function max(a,b:longint):longint;begin   if a>b then exit(a);   exit(b);end;begin   readln(n);   for i:=max(n-120,0) to n do   begin      x:=i;ans:=i;      while x>0 do      begin         ans:=ans+x mod 10;         x:=x div 10;      end;      if ans=n then begin inc(k);q[k]:=i;end;   end;   writeln(k);   for i:=1 to k do writeln(q[i]);end.