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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
#define INF 10000000000000000
#define pb push_back
#define sz(a) int((a).size())
#define all(c) c.begin(), c.end()
#define tr(c, i) for (typeof(c).begin() i = c.begin(); i != c.end(); i++)
#define present(c, x) (c.find(x) != c.end())
#define cpresent(c, x) (find(all(c), x) != c.end())
ll mod = 1e9 + 7;

ll bigmod(ll base, ll power)
{

    if (power == 0)
        return 1;
    ll x = bigmod(base, power / 2);

    if (power % 2 == 0)
        return (x * x) % mod;
    return (x * x * base) % mod;
}

int main()
{
    ll m,n,a,b;
    cin>>n;
    a = bigmod(10,n);
    b= bigmod(9,n) * 2;
    b = b%mod;
    a = (a-b) % mod;
    b = bigmod(8,n);
    a = (a+b) % mod;
    m = a;
    m = (m+10*mod)%mod;
    cout<<m<<endl;
    return 0;
}