{"raw_statement":[{"iden":"problem statement","content":"You are given an integer $W$.  \nYou are going to prepare some weights so that all of the conditions below are satisfied.\n\n*   The number of weights is between $1$ and $300$, inclusive.\n*   Each weight has a mass of positive integer not exceeding $10^6$.\n*   Every integer between $1$ and $W$, inclusive, is a **good integer**. Here, a positive integer $n$ is said to be a good integer if the following condition is satisfied:\n    *   We can choose **at most $3$** different weights from the prepared weights with a total mass of $n$.\n\nPrint a combination of weights that satisfies the conditions."},{"iden":"constraints","content":"*   $1 \\leq W \\leq 10^6$\n*   $W$ is an integer."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$W$"},{"iden":"sample input 1","content":"6"},{"iden":"sample output 1","content":"3\n1 2 3\n\nIn the output above, $3$ weights with masses $1$, $2$, and $3$ are prepared.  \nThis output satisfies the conditions. Especially, regarding the $3$\\-rd condition, we can confirm that every integer between $1$ and $W$, inclusive, is a good integer.\n\n*   If we choose only the $1$\\-st weight, it has a total mass of $1$.\n*   If we choose only the $2$\\-nd weight, it has a total mass of $2$.\n*   If we choose only the $3$\\-rd weight, it has a total mass of $3$.\n*   If we choose the $1$\\-st and the $3$\\-rd weights, they have a total mass of $4$.\n*   If we choose the $2$\\-nd and the $3$\\-rd weights, they have a total mass of $5$.\n*   If we choose the $1$\\-st, the $2$\\-nd, and the $3$\\-rd weights, they have a total mass of $6$."},{"iden":"sample input 2","content":"12"},{"iden":"sample output 2","content":"6\n2 5 1 2 5 1\n\nYou may prepare multiple weights with the same mass."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}