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;
#define ll long long
#define mod 1000000007

ll func(ll b, ll p)
{
    ll i, ans = 1;
    for(i=1;i<=p;i++){
        ans *= b;
        ans %= mod;
    }
    return ans;
}

int main()
{
    ll n,ans;
    scanf("%lld", &n);
    ans = (func(10,n)-(2*func(9,n))+func(8,n))%mod;
    ans = (ans+mod)%mod;
    printf("%lld\n", ans);
    return 0;
}