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 rep(i,n) for (int i=0;i<(n);i++)

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

ll modpow(ll a, ll b, ll mod = 1000000007) {
   ll res = 1;
   for (a %= mod; b; a = a * a % mod, b >>= 1)
     if (b & 1) res = res * a % mod;
   return res;
 }


int main(void)
{
    int64_t n,ans,a1,a2;

    cin >> n;

    a1 = modpow(10,n,1000000007) - modpow(9,n,1000000007);

    if(a1 < 0)a1+=1000000007;

    a1 *= 2;

    a1 %= 1000000007;

    a2 = modpow(10,n,1000000007) - modpow(8,n,1000000007);

    if(a2 < 0)a2+=1000000007;

    ans = a1-a2;

    if(ans < 0)ans+=1000000007;


    cout << ans << endl;
}