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>
#include <boost/multiprecision/cpp_int.hpp>

#define int long long

#define override_rep(i, l, r, mes, ...) mes
#define rep1(i, n) for (int i = 0; i < n; i++)
#define rep2(i, l, r) for (int i = l; i < r; i++)
#define rep(...) override_rep(__VA_ARGS__, rep2, rep1)(__VA_ARGS__)

using namespace std;
using P = pair<int, int>;
using ll = long long;
using ld = double;

using bint = boost::multiprecision::cpp_int;

constexpr int MOD = 1e9 + 7;

template<typename T, typename U>
istream& operator>>(istream& in, pair<T, U>& p) {
    in >> p.first >> p.second;
    return in;
}

// https://twitter.com/vane11ope ←フォローしましょう
// (ノ)>◡<(ヾ)ﾓﾁﾓﾁ
signed main(signed argc, char* argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int n;
    cin>>n;
    int a,b,c;
    a=0;
    b=2;
    c=8;
    rep(i,n-1){
        a=(a*10+b)%MOD;
        b=(b*9+c*2)%MOD;
        c=c*8%MOD;
    }
    cout<<a<<endl;
}