The union of sequences#2705

The union of sequences

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Easy

Given two infinite increasing sequences of numbers $A$ and $B$ . The $i$ -th term of sequence $A$ is $i^{2}$ i^2. The $i$ -th term of sequence $B$ is $i^{3}$ i^3.

Sequence $C$ is an increasing sequence obtained by merging sequences $A$ and $B$ . If a number appears in both sequence $A$ and sequence $B$ , it appears only once in sequence $C$ .

Input

The only line of the input file contains a natural number $x$ ( $1 \leq x \leq 1 0^{7}$ 1 \leq x \leq 10^7).

Output

Output $C_{x}$ C_x to the output file.

Examples

Example 1

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i^{2}

i^{3}

1 \leq x \leq 1 0^{7}

C_{x}