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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const ll MOD = 1e9 + 7;
int main()
{
    ll n, x=1, y=1, z=1;
    cin >> n;
    for(int i=1;i<=n;i++)
    {
        x*=10,y*=9,z*=8;
        x%=MOD,y%=MOD,z%=MOD;
    }
    x -= y;
    x = (x+MOD)%MOD;
    x -= y;
    x = (x+MOD)%MOD;
    x +=z;
    x %= MOD;
    x = (x+MOD)%MOD;
    cout << x << endl;
}