{"raw_statement":[{"iden":"statement","content":"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.\n\nSince 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."},{"iden":"input","content":"The first line contains integer _n_ (1 ≤ _n_ ≤ 109)."},{"iden":"output","content":"In the first line print one integer _k_ — number of different values of _x_ satisfying the condition.\n\nIn next _k_ lines print these values in ascending order."},{"iden":"examples","content":"Input\n\n21\n\nOutput\n\n1\n15\n\nInput\n\n20\n\nOutput\n\n0"},{"iden":"note","content":"In the first test case _x_ = 15 there is only one variant: 15 + 1 + 5 = 21.\n\nIn the second test case there are no such _x_."}],"translated_statement":[{"iden":"statement","content":"八年级学生沃瓦今天值日。下课后，他走进办公室擦黑板，发现上面写着一个数字 #cf_span[n]。他问这是什么数字，数学老师伊娜·彼得罗夫娜告诉他，#cf_span[n] 是一道给一年级学生的算术题的答案。教材中给出了某个 *正整数* #cf_span[x]，题目要求将 #cf_span[x] 加上其十进制表示下各位数字之和。\n\n由于黑板上的数字 #cf_span[n] 很小，沃瓦很快猜出了教材中可能的 #cf_span[x]。现在他希望得到一个程序，对于任意给定的 #cf_span[n]，找出所有满足条件的 #cf_span[x]，或确定这样的 #cf_span[x] 不存在。请为沃瓦编写这样一个程序。\n\n第一行包含一个整数 #cf_span[n]（#cf_span[1 ≤ n ≤ 109]）。\n\n第一行输出一个整数 #cf_span[k] —— 满足条件的不同 #cf_span[x] 值的个数。\n\n接下来的 #cf_span[k] 行，按升序输出这些值。\n\n在第一个测试用例中，#cf_span[x = 15] 是唯一解：#cf_span[15 + 1 + 5 = 21]。\n\n在第二个测试用例中，不存在这样的 #cf_span[x]。"},{"iden":"input","content":"第一行包含一个整数 #cf_span[n]（#cf_span[1 ≤ n ≤ 109]）。"},{"iden":"output","content":"第一行输出一个整数 #cf_span[k] —— 满足条件的不同 #cf_span[x] 值的个数。接下来的 #cf_span[k] 行，按升序输出这些值。"},{"iden":"examples","content":"输入21输出115输入20输出0"},{"iden":"note","content":"在第一个测试用例中，#cf_span[x = 15] 是唯一解：#cf_span[15 + 1 + 5 = 21]。在第二个测试用例中，不存在这样的 #cf_span[x]。"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z}^+ $ with $ 1 \\leq n \\leq 10^9 $.  \nLet $ s(x) $ denote the sum of the decimal digits of $ x \\in \\mathbb{Z}^+ $.  \n\n**Constraints**  \nWe seek all $ x \\in \\mathbb{Z}^+ $ such that:  \n$$\nx + s(x) = n\n$$\n\n**Objective**  \nFind the number $ k $ of such $ x $, and output them in ascending order. If no such $ x $ exists, output $ k = 0 $.","simple_statement":null,"has_page_source":false}