Problem Statement

In problems on AtCoder, you are often asked to:

find the answer modulo 998244353.

Here, we have $998244353 = 119 \times 2^{23} + 1.$ Related to this, solve the following prolem:

You are given an integer N.
Print the minimum possible value of a + b + c for a triple of $non-negative integers (a, b, c) satisfying N = a \times 2^b + c$.

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer.

Constraints

• $1 \leq N \leq 10^{18}$
• N is an integer.

Sample Input 1

998244353

Sample Output 1

143

We have $998244353 = 119 \times 2^{23} + 1$, in other words, the triple $(a, b, c) = (119, 23, 1) satisfies N = a \times 2^{b} + c$.
The value a+b+c for this triple is 143.
There is no such triple where $a+b+c \leq 142$, so 143 is the correct output.

Sample Input 2

1000000007

Sample Output 2

49483

We have $1000000007 = 30517 \times 2^{15} + 18951$, in other words, the triple $(a, b, c) = (30517, 15, 18951) satisfies N = a \times 2^{b} + c$.
The value a+b+c for this triple is 49483.
There is no such triple where $a+b+c \leq 49482$, so 49483 is the correct output.

Sample Input 3

1

Sample Output 3

1

Note that we have 2^0 = 1.

Sample Input 4

998984374864432412

Sample Output 4

2003450165

见题面 Input 部分

见题面 Output 部分