A. Add More Zero

Codeforces

IDCF10225A

Time1000ms

Memory128MB

Difficulty—

English · Original

Formal · Original

There is a youngster known for amateur propositions concerning several mathematical hard problems. Today 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). As 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). For ease of processing, all integers he would probably use in this interesting problem ought to be as computable as this supercomputer could. Given the positive integer $m$, your task is to determine maximum possible integer $k$ that is suitable for the specific supercomputer. The input contains multiple (about $10^5$) test cases. Each test case in only one line contains an integer $m$ ($1 <= m <= 10^5$). 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. ## Input The input contains multiple (about $10^5$) test cases.Each test case in only one line contains an integer $m$ ($1 <= m <= 10^5$). ## Output 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. [samples]

**Definitions** Let $ G = (V, E) $ be an undirected graph with $ |V| = n $ vertices (people) and $ |E| = m $ edges (friendship bonds). **Constraints** 1. $ 2 \leq n \leq 2 \times 10^3 $ 2. $ 0 \leq m \leq 2 \times 10^3 $ 3. Each edge connects two distinct vertices: $ \forall (a,b) \in E, a \ne b $ **Objective** Compute the **diameter** of $ G $, defined as: $$ k = \max_{u,v \in V} \operatorname{dist}(u,v) $$ where $ \operatorname{dist}(u,v) $ is the length of the shortest path between $ u $ and $ v $, or $ \infty $ if no path exists. If $ G $ is disconnected (i.e., $ \exists u,v \in V $ such that $ \operatorname{dist}(u,v) = \infty $), output "_=[_". Otherwise, output "_=]" followed by $ k $.

API Response (JSON)

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