142. Hydra Tree

Codeforces

IDCF10269142

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You have a tree that is growing very fast. At first, the tree has one branch. On each successive day, the tree grows a certain number of branches. On each day, the number of new branches is calculated as $n$ times $b$, where $b$ represents how many branches were on the tree on the previous day, and $n$ is a variable you have to calculate. $n$ will always be greater than one. At an unknown number of days, the tree has $x$ branches. Given this value, figure out the minimum possible value of $n$ used in the formula, given that the tree started out with exactly one branch. The only line of input contains a single positive integer $x$. $x$ will be less than 10000. Output a single positive integer $n$: the minimum possible value of $n$, greater than one, such that the tree could have $x$ branches at some point. $n$ has to stay the same throughout the entire process of growing the tree, i.e. it cannot change between days. ## Input The only line of input contains a single positive integer $x$. $x$ will be less than 10000. ## Output Output a single positive integer $n$: the minimum possible value of $n$, greater than one, such that the tree could have $x$ branches at some point. $n$ has to stay the same throughout the entire process of growing the tree, i.e. it cannot change between days. [samples]

**Definitions** Let $ x \in \mathbb{Z}^+ $ be the final number of branches, with $ x < 10000 $. Let $ n \in \mathbb{Z} $ be the constant growth multiplier, $ n > 1 $. The tree starts with 1 branch. On day $ k $, the number of branches is $ b_k = n \cdot b_{k-1} $, with $ b_0 = 1 $. Thus, after $ d $ days, $ b_d = n^d $, for some integer $ d \geq 1 $. **Constraints** 1. $ x = n^d $ for some integer $ d \geq 1 $. 2. $ n > 1 $. **Objective** Find the minimum integer $ n > 1 $ such that $ x = n^d $ for some integer $ d \geq 1 $.

API Response (JSON)

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