In-jae, did you catch Mushmom?

In-jae spent a year failing to defeat an orange mushroom, and now he sets out on an adventure to settle things with Mushmom.

In-jae has health $A$ and attack $B$. Mushmom has health $X$ and attack $Y$.

In-jae attacks first. The two take turns, and each may take one action per turn.

There are only three kinds of action.

• Attack: deals damage equal to the current attack.
• Counter: takes no damage this turn and deals damage equal to the opponent's attack. Health increases by 10% of the current health. Discard any fraction.
• Buff: raises the current attack by 20% and triples the damage taken this turn only. Discard any fraction.

Mushmom can only attack.

Help In-jae find the way to hunt Mushmom in as few turns as possible.

On the first line, input In-jae's health $A$ and attack $B$, then Mushmom's health $X$ and attack $Y$, in that order.

($1 \le A, X \le 100{,}000$, $1 \le B, Y \le 10{,}000$)

On the first line, print the number of actions In-jae takes when Mushmom is hunted in the fewest possible actions.