You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 3.0 seconds
Memory limit: 256.0 MB

# Problem
Bogocubic is playing a game with amenotiomoi. First, Bogocubic fixed an integer $$$n$$$, and then he gave amenotiomoi an integer $$$x$$$ which is initially equal to $$$1$$$.

In one move amenotiomoi performs one of the following operations with the same probability:

- increase $$$x$$$ by $$$1$$$;
- multiply $$$x$$$ by $$$2$$$.

Bogocubic wants to find the expected number of moves amenotiomoi has to do to make $$$x$$$ greater than or equal to $$$n$$$. Help him find this number modulo $$$998\,244\,353$$$.

Formally, let $$$M = 998\,244\,353$$$. It can be shown that the answer can be expressed as an irreducible fraction $$$\frac{p}{q}$$$, where $$$p$$$ and $$$q$$$ are integers and $$$q \not \equiv 0 \pmod{M}$$$. Output the integer equal to $$$p \cdot q^{-1} \bmod M$$$. In other words, output such an integer $$$y$$$ that $$$0 \le y < M$$$ and $$$y \cdot q \equiv p \pmod{M}$$$.

## Input Format
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The only line of each test case contains one integer $$$n$$$ ($$$1 \le n \le 10^{18}$$$).

## Output Format
For each test case, output a single integer — the expected number of moves modulo $$$998\,244\,353$$$.

## Examples
```input
7
1
4
8
15
998244353
296574916252563317
494288321850420024
```
```output
0
499122179
717488133
900515847
93715054
44488799
520723508
```

## Note
In the first test case, $$$n\le x$$$ without any operations, so the answer is $$$0$$$.

In the second test case, for $$$n = 4$$$, here is the list of all possible sequences of operations and their probabilities:

- $$$1\stackrel{+1}{\longrightarrow}2\stackrel{+1}{\longrightarrow}3\stackrel{+1}{\longrightarrow}4$$$, the probability is $$$\frac{1}{8}$$$;
- $$$1\stackrel{\times 2}{\longrightarrow}2\stackrel{+1}{\longrightarrow}3\stackrel{+1}{\longrightarrow}4$$$, the probability is $$$\frac{1}{8}$$$;
- $$$1\stackrel{+1}{\longrightarrow}2\stackrel{+1}{\longrightarrow}3\stackrel{\times 2}{\longrightarrow}6$$$, the probability is $$$\frac{1}{8}$$$;
- $$$1\stackrel{\times 2}{\longrightarrow}2\stackrel{+1}{\longrightarrow}3\stackrel{\times 2}{\longrightarrow}6$$$, the probability is $$$\frac{1}{8}$$$;
- $$$1\stackrel{+1}{\longrightarrow}2\stackrel{\times 2}{\longrightarrow}4$$$, the probability is $$$\frac{1}{4}$$$;
- $$$1\stackrel{\times 2}{\longrightarrow}2\stackrel{\times 2}{\longrightarrow}4$$$, the probability is $$$\frac{1}{4}$$$.

So the expected number of moves is $$$4 \cdot \left(3 \cdot \frac{1}{8}\right) + 2 \cdot \left(2 \cdot \frac{1}{4} \right) =\frac{5}{2} \equiv 499122179 \pmod{998244353}$$$.

In the third test case, for $$$n = 8$$$, the expected number of moves is $$$\frac{137}{32}\equiv 717488133\pmod{998244353}$$$.

In the fourth test case, for $$$n = 15$$$, the expected number of moves is $$$\frac{24977}{4096} \equiv 900515847 \pmod{998244353}$$$.

Now solve the problem and return the code.