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,a,...) for(int i = (a)*(strlen(#__VA_ARGS__)!=0);i<(int)(strlen(#__VA_ARGS__)?__VA_ARGS__:(a));++i)
#define per(i,a,...) for(int i = (strlen(#__VA_ARGS__)?__VA_ARGS__:(a))-1;i>=(int)(strlen(#__VA_ARGS__)?(a):0);--i)
#define foreach(i, n) for(auto &i:(n))
#define all(x) (x).begin(), (x).end()
#define bit(x) (1ll << (x))
#define lambda(RES_TYPE, ...) (function<RES_TYPE(__VA_ARGS__)>)[&](__VA_ARGS__) -> RES_TYPE
#define method(FUNC_NAME, RES_TYPE, ...) function<RES_TYPE(__VA_ARGS__)> FUNC_NAME = lambda(RES_TYPE, __VA_ARGS__)
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
const ll MOD = (ll)1e9+7;
//const ll MOD = 998244353;
const int INF = (ll)1e9+7;
const ll INFLL = (ll)1e18;
template<class t>
using vvector = vector<vector<t>>;
template<class t>
using vvvector = vector<vector<vector<t>>>;
template<class t>
using priority_queuer = priority_queue<t, vector<t>, greater<t>>;
template<class t, class u> bool chmax(t &a, u b){if(a<b){a=b;return true;}return false;}
template<class t, class u> bool chmin(t &a, u b){if(a>b){a=b;return true;}return false;}
#ifdef DEBUG
#define debug(x) cout<<"LINE "<<__LINE__<<": "<<#x<<" = "<<x<<endl;
#else
#define debug(x) (void)0
#endif

namespace templates{
  ll modpow(ll x, ll b){
    ll res = 1;
    while(b){
      if(b&1)res = res * x % MOD;
      x = x * x % MOD;
      b>>=1;
    }
    return res;
  }

  ll modinv(ll x){
    return modpow(x, MOD-2);
  }

  bool was_output = false;
  template<class t>
  void output(t a){
    if(was_output)cout << " ";
    cout << a;
    was_output = true;
  }
  void outendl(){
    was_output = false;
    cout << endl;
  }
  ll in(){
    ll res;
    scanf("%lld", &res);
    return res;
  }

  template<class t>
  istream& operator>>(istream&is, vector<t>&x){
    for(auto &i:x)is >> i;
    return is;
  }

  template<class t, class u>
  istream& operator>>(istream&is, pair<t, u>&x){
    is >> x.first >> x.second;
    return is;
  }

  template<class t>
  void in(t&x){
    cin >> x;
  }

  template<class t>
  t in(){
    t res; cin >> res; return res;
  }

  template<class t>
  void out(t x){
    cout << x;
  }

  template<class t>
  vector<t> sorted(vector<t> line,function<bool(t,t)> comp=[](t a,t b){return a<b;}){
    sort(line.begin(),line.end(),comp);
    return line;
  }

  template<class t>
  vector<t> reversed(vector<t> line){
    reverse(line.begin(),line.end());
    return line;
  }
}

using namespace templates;

template<long long mod>
class modint{
	public:
		long long x;
		modint(long long a){x=a%mod;if(x<0)x+=mod;}
		modint(){x=0;}

		modint pow(long long a){
			modint res(1), b(x);
			while(a){
				if(a&1)res*=b;
				b*=b;
				a>>=1;
			}
			return res;
		}

		modint inv(){return pow(mod-2);}

		modint& operator+=(modint a){x=(x+a.x)%mod;return *this;}
		modint& operator-=(modint a){x=x-a.x;if(x<0)x+=mod;return *this;}
		modint& operator*=(modint a){x=x*a.x%mod;return *this;}
		modint& operator/=(modint a){x=x*a.inv().x%mod;return *this;}

		modint operator+(modint a){return modint(x)+=a;}
		modint operator-(modint a){return modint(x)-=a;}
		modint operator*(modint a){return modint(x)*=a;}
		modint operator/(modint a){return modint(x)/=a;}

		modint operator-(){return modint(x);}

		bool operator==(const modint a){return x == a.x;}
		bool operator<(const modint a){return x < a.x;}
		bool operator>(const modint a){return x > a.x;}
};

template<long long mod>
ostream& operator<<(ostream& os, const modint<mod>& a){
	os << a.x;
	return os;
}

using mint = modint<MOD>;

mint func(){
    ll n = in();
    vvector<mint> dp(n,vector<mint>(4,0));
    vvector<bool> used(n,vector<bool>(4,0));
    method(func,mint,int place,int sum){
        if(place==n){
            return sum == 3;
        }
        mint &it = dp[place][sum];
        if(used[place][sum])return it;
        used[place][sum] = true;
        it = 0;
        it += func(place+1,sum|1);
        it += func(place+1,sum|2);
        it += func(place+1,sum) * 8;
        return it;
    };
    per(i,n){
        func(i,0);
    }
    return func(0,0);
}

int main(){
    cout << func() << endl;
  return 0;
}