{"raw_statement":[{"iden":"statement","content":"There is a youngster known for amateur propositions concerning several mathematical hard problems.\n\nToday he is going to prepare a thought-provoking problem on a specific type of supercomputer which has the ability to support calculating operations for integers between $0$ and $(2^m -1)$ (inclusive).\n\nAs a young man born with ten fingers, he loves the powers of $10$ so much, which results in his eccentricity that he always ranges integers he would like to use from $1$ to $10^k$ (inclusive).\n\nFor ease of processing, all integers he would probably use in this interesting problem ought to be as computable as this supercomputer could.\n\nGiven the positive integer $m$, your task is to determine maximum possible integer $k$ that is suitable for the specific supercomputer.\n\nThe input contains multiple (about $10^5$) test cases.\n\nEach test case in only one line contains an integer $m$ ($1 <= m <= 10^5$).\n\nFor each test case, output \"_Case #x: y_\" in one line (without quotes), where $x$ indicates the case number starting from $1$, and $y$ denotes the answer to the corresponding case.\n\n"},{"iden":"input","content":"The input contains multiple (about $10^5$) test cases.Each test case in only one line contains an integer $m$ ($1 <= m <= 10^5$)."},{"iden":"output","content":"For each test case, output \"_Case #x: y_\" in one line (without quotes), where $x$ indicates the case number starting from $1$, and $y$ denotes the answer to the corresponding case."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ G = (V, E) $ be an undirected graph with $ |V| = n $ vertices (people) and $ |E| = m $ edges (friendship bonds).  \n\n**Constraints**  \n1. $ 2 \\leq n \\leq 2 \\times 10^3 $  \n2. $ 0 \\leq m \\leq 2 \\times 10^3 $  \n3. Each edge connects two distinct vertices: $ \\forall (a,b) \\in E, a \\ne b $  \n\n**Objective**  \nCompute the **diameter** of $ G $, defined as:  \n$$\nk = \\max_{u,v \\in V} \\operatorname{dist}(u,v)\n$$  \nwhere $ \\operatorname{dist}(u,v) $ is the length of the shortest path between $ u $ and $ v $, or $ \\infty $ if no path exists.  \n\nIf $ G $ is disconnected (i.e., $ \\exists u,v \\in V $ such that $ \\operatorname{dist}(u,v) = \\infty $), output \"_=[_\".  \nOtherwise, output \"_=]\" followed by $ k $.","simple_statement":"Given n people and m friendship bonds, find the minimum k such that any two people are connected through at most k friendships. If not everyone is connected, print \"_=[_\". Otherwise, print \"_=]_ k\".","has_page_source":false}