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>
#define fast ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)
#define ll long long int
#define ld long double
using namespace std;
const int N = 1e6 + 5;
const int MOD = 1e9 + 7;

ll power(ll x, ll y){
    x %= MOD;
    ll ans = 1;
    while(y){
        if(y & 1)
            ans = (ans * x) % MOD;
        y >>= 1LL;
        x = (x * x) % MOD;
    }
    return ans;
}
ll ad(ll a, ll b){
    return((a % MOD + b % MOD) % MOD);
}
ll sub(ll a, ll b){
    return((a % MOD - b % MOD + MOD) % MOD);
}
ll mul(ll a, ll b){
    return(((a % MOD) * (b % MOD)) % MOD);
}
ll divi(ll a, ll b){
    return(mul(a, power(b, MOD - 2)) % MOD);
}

int main(){
	fast;
	ll n;
	cin >> n;
	cout << sub(ad(power(10, n), power(8, n)), ad(power(9, n), power(9, n)));
	return 0;
}