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 <atcoder/all>
using namespace std;
// using namespace atcoder;
 
#define rp(i, k, n) for (int i = k; i < n; i++)
using ll = long long;
using ld = double;

template<class T>inline bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>inline bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
const ll INF = 1ll << 60;
const ll MOD = 1e9 + 7ll;
const double PI=3.14159265358979323846;

ll mypow(ll X, ll n) {  // 繰り返し２乗法　計算量log(n)
    if(n == 0) return 1ll;
    ll Y = mypow(X, n/2);
    if(n % 2 == 1) return X * Y % MOD * Y % MOD;
    else return Y * Y % MOD;
}


int main() {
    ll n; cin >> n;
    ll res = mypow(10, n);
    res = (((res - 2 * mypow(9, n))%MOD)+MOD)%MOD;
    res = (res + mypow(8, n))%MOD;
    cout << res << endl;
    return 0;
}