{"raw_statement":[{"iden":"statement","content":"Given an integer n, find out number of ways to represent it as the sum of two or more integers ai with the next property: ratio ai / ai - 1 is the same positive integer for all possible i > 1.\n\nInput consists of one integer n (1 ≤ n ≤ 105).\n\nPrint one integer — number of representations.\n\nIn the first sample no such representation exists.\n\nIn the second sample there exist two representations:\n\n"},{"iden":"input","content":"Input consists of one integer n (1 ≤ n ≤ 105)."},{"iden":"output","content":"Print one integer — number of representations."},{"iden":"examples","content":"Input1Output0Input5Output2Input567Output21"},{"iden":"note","content":"In the first sample no such representation exists.In the second sample there exist two representations:  1 1 1 1 1, then q = 1.  1 4, then q = 4. "}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ with $ 1 \\leq n \\leq 10^5 $.  \nA representation of $ n $ is a sequence of integers $ (a_1, a_2, \\dots, a_k) $ with $ k \\geq 2 $, such that:  \n- $ \\sum_{i=1}^k a_i = n $,  \n- $ a_i \\in \\mathbb{Z}^+ $ for all $ i $,  \n- $ \\frac{a_i}{a_{i-1}} = r $ for all $ i \\in \\{2, \\dots, k\\} $, where $ r \\in \\mathbb{Z}^+ $ is a constant ratio.\n\n**Objective**  \nCount the number of such sequences $ (a_1, a_2, \\dots, a_k) $ satisfying the above conditions.","simple_statement":"Count the number of ways to write n as a sum of two or more integers where each term divided by the previous one is the same positive integer.","has_page_source":false}