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 all(x) begin(x), end(x)
#define dbg(x) cerr << #x << " = " << x << endl
#define _ << ' ' <<
using namespace std;
using ll = long long;
using vi = vector<int>;

const int mod = 1000000007;
int add(int a, int b) { return (a += b) < mod? a : a - mod; }
int sub(int a, int b) { return (a -= b) >=  0? a : a + mod; }
int mul(int a, int b) { return 1LL * a * b % mod; }
void adds(int& a, int b) { a = add(a, b); }
void subs(int& a, int b) { a = sub(a, b); }
void muls(int& a, int b) { a = mul(a, b); }
void maxs(int& a, int b) { a = max(a, b); }
void mins(int& a, int b) { a = min(a, b); }
int pwr(int a, ll p) {
    if (p == 0) return 1;
    if (p & 1) return mul(a, pwr(a, p - 1));
    return pwr(mul(a, a), p / 2);
}
int inv(int a) { return pwr(a, mod - 2); }
int neg(int a) { return sub(0, a); }

int dp[1000005][2][2];
int n;

int f(int x, int p, int q)
{
    if (x == n)
        return p + q == 2;
    if (dp[x][p][q] != -1)
        return dp[x][p][q];
    
    int sol = 0;
    for (int i = 0; i <= 9; ++i)
        adds(sol, f(x + 1, p || (i == 0), q || (i == 9)));
    return dp[x][p][q] = sol;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    memset(dp, -1, sizeof dp);
    cout << f(0, 0, 0);
}