Problem:
Score : 300 points

Problem Statement

How many integer sequences A_1,A_2,\ldots,A_N of length N satisfy all of the following conditions?

0 \leq A_i \leq 9

There exists some i such that A_i=0 holds.

There exists some i such that A_i=9 holds.

The answer can be very large, so output it modulo 10^9 + 7.

Constraints

1 \leq N \leq 10^6

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer modulo 10^9 + 7.

Sample Input 1

2

Sample Output 1

2

Two sequences \{0,9\} and \{9,0\} satisfy all conditions.

Sample Input 2

1

Sample Output 2

0

Sample Input 3

869121

Sample Output 3

2511445

Solution in PHP (7.4.4) (judge verdict: Accepted)

<?php

[$N] = fscanf(STDIN, "%d");
$ans = 1;
const MOD = 1000000007;
for($i=0;$i<$N;$i++){
    $ans *= 10;
    $ans %= MOD;
}
$hiku = 1;
$tasu = 1;
for($i=0;$i<$N;$i++){
    $hiku *= 9;
    $tasu *= 8;
    $hiku %= MOD;
    $tasu %= MOD;
}
$ans -= ($hiku + $hiku - $tasu) % MOD;
$ans  = (int)gmp_mod($ans,  MOD);
echo $ans;