{"problem":{"name":"119 × 2^23 + 1","description":{"content":"In problems on AtCoder, you are often asked to: > find the answer modulo $998244353$. Here, we have $998244353 = 119 \\times 2^{23} + 1$. Related to this, solve the following prolem: > You are given","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc119_a"},"statements":[{"statement_type":"Markdown","content":"In problems on AtCoder, you are often asked to:\n\n> find the answer modulo $998244353$.\n\nHere, we have $998244353 = 119 \\times 2^{23} + 1$. Related to this, solve the following prolem:\n\n> You are given an integer $N$.  \n> Print the minimum possible value of $a + b + c$ for a triple of non-negative integers $(a, b, c)$ satisfying $N = a \\times 2^b + c$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{18}$\n*   $N$ is an integer.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc119_a","tags":[],"sample_group":[["998244353","143\n\nWe have $998244353 = 119 \\times 2^{23} + 1$, in other words, the triple $(a, b, c) = (119, 23, 1)$ satisfies $N = a \\times 2^{b} + c$.  \nThe value $a+b+c$ for this triple is $143$.  \nThere is no such triple where $a+b+c \\leq 142$, so $143$ is the correct output."],["1000000007","49483\n\nWe have $1000000007 = 30517 \\times 2^{15} + 18951$, in other words, the triple $(a, b, c) = (30517, 15, 18951)$ satisfies $N = a \\times 2^{b} + c$.  \nThe value $a+b+c$ for this triple is $49483$.  \nThere is no such triple where $a+b+c \\leq 49482$, so $49483$ is the correct output."],["1","1\n\nNote that we have $2^0 = 1$."],["998984374864432412","2003450165"]],"created_at":"2026-03-03 11:01:14"}}