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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{input, fastout};

#[fastout]
fn main() {
    input!{
        n: usize
    }
    //n c 2 == n * (n-1) / 2
    // 10 ^ (n - 2)

    let ans = ModInt::from_usize(10).pow(n) + ModInt::from_usize(8).pow(n) - ModInt::from_usize(9).pow(n) * ModInt::from_usize(2);
    println!("{}", ans.val());
}

use std::ops::*;

const MOD: usize = 1000000007;
#[derive(Copy, Clone)]
struct ModInt {
    n: usize,
}

impl ModInt {
    fn val(self)->usize {
        self.n
    }
    fn from_usize(n: usize) -> ModInt {
        ModInt { n: n % MOD }
    }
    fn pow(self, power: usize) -> ModInt {
        if power == 0 {
            return ModInt::from_usize(1);
        }
        if power % 2 == 0 {
            let t = self.pow(power/2);
            return t * t;
        }
        self * self.pow(power-1)
    }
    fn inv(self) -> ModInt {
        self.pow(MOD - 2)
    }
}

impl Add for ModInt {
    type Output = ModInt;

    fn add(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n += rhs.n;
        if tmp.n >= MOD {
            tmp.n -= MOD;
        }
        tmp
    }
}

impl AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl Sub for ModInt {
    type Output = ModInt;

    fn sub(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        if tmp.n < rhs.n {
            tmp.n += MOD;
        }
        tmp.n -= rhs.n;
        tmp
    }
}

impl SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl Mul for ModInt {
    type Output = ModInt;

    fn mul(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n *= rhs.n;
        tmp.n %= MOD;
        tmp
    }
}

impl MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n *= rhs.inv().n;
        tmp.n %= MOD;
        tmp
    }
}

impl DivAssign for ModInt {
    fn div_assign(&mut self, rhs: ModInt) {
        *self = *self / rhs;
    }
}