A10408 | Bear and Tower of Cubes

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 $a^{3}$ . A tower consisting of blocks with sides $a_{1},a_{2},...,a_{k}$ has the total volume $a_{1}^{3}+a_{2}^{3}+...+a_{k}^{3}$ .

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.

The only line of the input contains one integer $m$ ( $1<=m<=10^{15}$ ), meaning that Limak wants you to choose $X$ between $1$ and $m$ , inclusive.

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.