House of Cards

Susan wants to build a house of cards so big that the whole country would be buried in cards if it toppled over.

The house has a triangular shape. The photo above shows a house of height 6.

A house of height $h$ is built from $h$ rows. Counting from the top, row $i$ consists of $i$ pairs of cards leaning against each other, so it uses $2i$ cards. Between row $i$ and row $i+1$ lie $i$ flat cards. The total number of cards in a house of height $h$ is therefore

$\frac{h(3h+1)}{2}$

The figure above shows the structure of a house of height 5, which uses 40 cards.

For the house to look right, the four suits (clubs, diamonds, hearts, spades) must appear equally often. Depending on the height, that is sometimes possible and sometimes not. Given a lower bound $h_0$ on the height, find the smallest height $h \ge h_0$ for which such a house can be built.

The first line contains an integer $h_0$, the minimum height of the house ($1 \le h_0 \le 10^{1000}$).

Print the smallest height $h \ge h_0$ for which a house can be built using each of the four suits equally often.