**Time limit:**1.00 s**Memory limit:**512 MB

Two grids are considered to be different if it is not possible to rotate one of them so that they look the same.

**Input**

The only input line has an integer $n$: the size of the grid.

**Output**

Print one integer: the number of grids modulo $10^9+7$.

**Constraints**

- $1 \le n \le 10^9$

**Example**

Input:

`4`

Output:

`16456`