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A. Vanya and Cubes

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVanya got *n* cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the *i*-th level of the pyramid must have 1 + 2 + ... + (*i* - 1) + *i* cubes.

Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{4}) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Examples

Input

1

Output

1

Input

25

Output

4

Note

Illustration to the second sample:

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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