Pseudo-dichotomic search P60373

Consider a hidden vector $V$ with $n$ integer numbers in strictly increasing order. Given an integer $x$ that belongs to $V$, you will play a game to guess the position $j$ where $V[j] = x$. You have to use a “black box” $B$, with parameters $x$ and a position $i$ inside $V$. If there is a $j \in \{i - 1, i, i + 1 \}$ such that $V[j] = x$, you win the game. Otherwise, $B$ will tell you whether $x < V[i-1]$ or $x > V[i+1]$.

Given $n$, what is the minimum number of calls to $B$ to win the game?

Input

Input consists of several cases, each one with an $n$ between 1 and $10^{18}$.

Output

For every $n$, print the worst-case number of calls to $B$ to win the game, assuming a strategy that minimizes that worst-case cost.