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;
typedef long long ll;
const int MOD = 1e9+7;
const int MAX = 1e6+10;
ll n;
ll dp[MAX][2][2];
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>n;
    dp[2][1][1]=2;
    dp[2][0][1]=17;
    dp[2][1][0]=17;
    dp[2][0][0]=64;
    for(int i=3;i<=n;i++){
        dp[i][0][0]+=(dp[i-1][0][0]*8)%MOD;
        dp[i][0][0]%=MOD;
        dp[i][1][0]+=(dp[i-1][1][0]*9+dp[i-1][0][0])%MOD;
        dp[i][1][0]%=MOD;
        dp[i][0][1]+=(dp[i-1][0][0]+dp[i-1][0][1]*9)%MOD;
        dp[i][0][1]%=MOD;
        dp[i][1][1]+=(dp[i-1][1][1]*10+dp[i-1][1][0]+dp[i-1][0][1])%MOD;
        dp[i][1][1]%=MOD;
    }
    cout<<dp[n][1][1]%MOD<<endl;
    return ~~(0^0);
}