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;
constexpr int Inf = 2000000010;
constexpr ll INF= 2000000000000000000;
constexpr ll MOD = 1000000007;
const double PI = 3.1415926535897;
typedef pair<int,int> P;
typedef pair<int,P> PP;

template<class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}

template<class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}

void mod(ll &val, ll M) {
    val = val % M;
    if(val < 0) {
        val += M;
    }
}

template<typename T>
T RS(T N, T P, T M){
    if(P == 0) {
        return 1;
    }
    if(P < 0) {
        return 0;
    }
    if(P % 2 == 0){
        ll t = RS(N, P/2, M);
        if(M == -1) return t * t;
        return t * t % M;
    }
    if(M == -1) {
        return N * RS(N,P - 1,M);
    }
    return N * RS(N, P-1, M) % M;
}

int main() {
    ll N;
    cin >> N;
    if(N == 1) {
        cout << 0 << endl;
        return 0;
    }
    ll ret = RS(10ll,N,MOD) - 2 * RS(9ll,N,MOD);
    mod(ret,MOD);
    ret = ret + RS(8ll,N,MOD);
    mod(ret,MOD);
    cout << ret << endl;
}