Codeforces Round #493 (Div. 1) C. Sky Full of Stars

C. Sky Full of Stars

time limit per test

4 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

On one of the planets of Solar system, in Atmosphere University, many students are fans of bingo game.

It is well known that one month on this planet consists of ${\mathrm{n2n2 days,\; so\; calendars,\; represented\; as\; square\; matrix nn by nn are\; extremely\; popular.}}^{}$

Weather conditions are even more unusual. Due to the unique composition of the atmosphere, when interacting with sunlight, every day sky takes one of three colors: blue, green or red.

To play the bingo, you need to observe the sky for one month — after each day, its cell is painted with the color of the sky in that day, that is, blue, green or red.

At the end of the month, students examine the calendar. If at least one row or column contains only cells of one color, that month is called lucky.

Let's call two colorings of calendar different, if at least one cell has different colors in them. It is easy to see that there are ${\mathrm{3n\cdot n3n\cdot n different\; colorings.\; How\; much\; of\; them\; are\; lucky?\; Since\; this\; number\; can\; be\; quite\; large,\; print\; it\; modulo 998244353998244353.}}^{}$

Input

The first and only line of input contains a single integer $\mathrm{nn (1\le n\le 10000001\le n\le 1000000) —\; the\; number\; of\; rows\; and\; columns\; in\; the\; calendar.}$

Output

Print one number — number of lucky colorings of the calendar modulo $998244353998244353$

Examples

input

Copy

1

output

Copy

3

input

Copy

2

output

Copy

63

input

Copy

3

output

Copy

9933

Note

In the first sample any coloring is lucky, since the only column contains cells of only one color.

In the second sample, there are a lot of lucky colorings, in particular, the following colorings are lucky:

While these colorings are not lucky:

思路：容斥，枚举行内一致以及列内一致的个个数，用二项式化简消掉一维，另一维直接枚举就行了。要用快速幂，nlogn，不知道官方题解O(n)是怎么做到的。