Aztec Pyramid

문제

Aztec emperor Cuitláhuac is going to build a pyramid in his honor. This pyramid should be taller than previous ones.

The Aztec pyramid is build out of stone blocks. Each block is 1×1×1-hunab cube. Cuitláhuac places first block on the ground during the foundation ceremony. Each of the following blocks must share a face with at least one of the previous blocks.

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The block is stable if it stands on the ground, or it stands on another block, that has a block or the ground next to each face. To stand the test of time the pyramid must be stable i.e. each block of it must be stable.

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Cuitláhuac asks you to determine the height of the tallest stable pyramid that can be built out of available blocks.

입력

The only line of the input file contains a single integer number n — the number of available blocks, including the first one (1 ≤ n ≤ 10⁹).

출력

Output the height of the tallest stable pyramid that may be built out of n blocks. The height must be output in hunabs.