Pseudo-dichotomic search

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.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:06:03.181Z