Problem B
Save the Planets

Image taken from commons.wikimedia.org/

Balatro is a game that has attracted many, not least of whom is Elvar. Elvar loves to play Balatro and is now in the middle of a game which has a good chance of beating his high score. The goal of Balatro is beating blinds by playing poker hands to get to a target score $x$. All poker hands have different numbers of chips and multipliers. The total score for a poker hand is then calculated as chips $\cdot $ multiplier. For example if you have $50$ chips and multiplier $4$ you get $200$ points for that hand. After each blind you can then buy jokers, tarot cards and planet cards to make your poker hands stronger, with the goal of scoring more points.

This game Elvar is playing with a special deck called plasma deck. When playing with this deck, instead of multiplying chips and the multiplier, you first average them and then multiply. For example if you have $50$ chips and multiplier $4$ like before, they are first averaged. Then you have $27$ chips and multiplier $27$, making your score $729$.

Elvar has been quite lucky in this Balatro game and managed to fetch the good old Perkeo early in the game. Thus he has decided he will try to collect copies of the planet card Neptune with the intent of finding Observatory. Elvar has managed to arrange his deck such that he always manages to play a Royal flush which gives him $151$ chips and a multiplier of $8$. He also knows that if he uses a Neptune card he adds $40$ chips and a multiplier of $4$ to that. For example if he uses two Neptune cards, a royal flush gets him $231$ chips and a multiplier of $16$, which after accounting for the plasma deck nets $123.5$ chips and a multiplier of $123.5$.

But now Elvar is in a bit of a pickle. He was so sure he would find the Observatory after the last blind that he sold all his jokers. But unfortunately the Observatory was nowhere to be found. Saddened by this he tried to make the best of a bad situation and bought the joker Constellation. What makes this joker good is that after each hand, before the score is counted, this joker multiplies the multiplier by $1 + 0.1 \cdot $ number of planet cards used. So if Elvar uses $10$ Neptune cards, he gets $551$ chips and a multiplier of $96$, which when accounting for the plasma deck becomes $323.5$ chips and a multiplier of $323.5$, which gives a score of $104,652.25$. Since Elvar is still in a bit of a shock from not finding the Observatory he doesn’t know how many cards he needs to use. Can you help him figure out the minimum number of planet cards he needs to use to win the blind?

Input

The input contains a single positive integer $x$, the number of points Elvar has to score to win the blind.

Output

Print the smallest number of planet cards Elvar has to use to win the blind.

Scoring

1337

0

55351

7

8739832

77