Bear and Tower of Cubes

2000ms

262144K

Description:

Limak is a little polar bear. He plays by building towers from blocks. Every block is a cube with positive integer length of side. Limak has infinitely many blocks of each side length.

A block with side a has volume a³. A tower consisting of blocks with sides a₁, a₂, ..., a_k has the total volume a₁³ + a₂³ + ... + a_k³.

Limak is going to build a tower. First, he asks you to tell him a positive integer X — the required total volume of the tower. Then, Limak adds new blocks greedily, one by one. Each time he adds the biggest block such that the total volume doesn't exceed X.

Limak asks you to choose X not greater than m. Also, he wants to maximize the number of blocks in the tower at the end (however, he still behaves greedily). Secondarily, he wants to maximize X.

Can you help Limak? Find the maximum number of blocks his tower can have and the maximum X ≤ m that results this number of blocks.

Input:

The only line of the input contains one integer m (1 ≤ m ≤ 10¹⁵), meaning that Limak wants you to choose X between 1 and m, inclusive.

Output:

Print two integers — the maximum number of blocks in the tower and the maximum required total volume X, resulting in the maximum number of blocks.

Sample Input:

Sample Output:

9 42

Sample Input:

Sample Output:

6 6

Note:

In the first sample test, there will be 9 blocks if you choose X = 23 or X = 42. Limak wants to maximize X secondarily so you should choose 42.

In more detail, after choosing X = 42 the process of building a tower is:

Limak takes a block with side 3 because it's the biggest block with volume not greater than 42. The remaining volume is 42 - 27 = 15.
The second added block has side 2, so the remaining volume is 15 - 8 = 7.
Finally, Limak adds 7 blocks with side 1, one by one.

So, there are 9 blocks in the tower. The total volume is is 3³ + 2³ + 7·1³ = 27 + 8 + 7 = 42.

Informação

Provedor Codeforces

Código CF679B