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 <stdio.h>
#define MOD         1000000007  /* 10^9 + 7 */
typedef long long ll;
ll MODPOW(ll a, ll n){ ll ans=1; while(n){if(n&1){ans=ans*a%MOD;} a=a*a%MOD; n>>=1; } return ans; }

int main(){
    ll n,ans=0;
    scanf("%lld",&n);
    ans = MODPOW(10,n) - MODPOW(9,n) - MODPOW(9,n) + MODPOW(8,n);
    ans%=MOD;
    ans=(ans+MOD)%MOD;
    printf("%lld\n",ans);
    return 0;
}