Bob is playing with binary strings. He defines two strings and to be similar if at least one of the following conditions holds:

- The lengths of both and must be divisible by . Let denote the first half of , and denote the second half. Similarly, define and as the first and second halves of . Then and are similar if either:
- is similar to and is similar to or
- is similar to and is similar to

If both conditions do not hold then and are not similar.

Bob begins to wonder about particular lengths of binary strings. These lengths are .

For each , Bob generates all possible binary strings of length . He wonders how many **ordered** pairs of binary strings from his set are similar. Since these numbers may be massive, print the answers modulo .

#### Constraints

In all subtasks,

##### Subtask 1 [5%]

##### Subtask 2 [10%]

All the are odd integers.

##### Subtask 3 [15%]

##### Subtask 4 [10%]

##### Subtask 5 [30%]

##### Subtask 6 [30%]

#### Input Specification

The first line contains a single integer, .

lines follow, the -th of which containing a single integer, .

#### Output Specification

Output lines, the -th of which containing the answer modulo for binary strings of length

#### Sample Input

```
1
2
```

#### Sample Output

`6`

#### Sample Input 2

```
2
3
4
```

#### Sample Output 2

```
8
54
```

#### Explanation for Sample Input 2

There are a total of ordered pairs of similar strings for binary strings of length , and there are a total of ordered pairs of similar strings for binary strings of length .

## Comments