Problem:
Score : 300 points

Problem Statement

There is a grid with infinitely many rows and columns. In this grid, there is a rectangular region with consecutive N rows and M columns, and a card is placed in each square in this region.
The front and back sides of these cards can be distinguished, and initially every card faces up.

We will perform the following operation once for each square contains a card:

For each of the following nine squares, flip the card in it if it exists: the target square itself and the eight squares that shares a corner or a side with the target square.

It can be proved that, whether each card faces up or down after all the operations does not depend on the order the operations are performed.
Find the number of cards that face down after all the operations.

Constraints

1 \leq N,M \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of cards that face down after all the operations.

Sample Input 1

2 2

Sample Output 1

0

We will flip every card in any of the four operations. Thus, after all the operations, all cards face up.

Sample Input 2

1 7

Sample Output 2

5

After all the operations, all cards except at both ends face down.

Sample Input 3

314 1592

Sample Output 3

496080

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    let (n, m): (usize, usize) = readln();
    let a = min(n, m);
    let b = max(n, m);
    if a == 1 {
        if b == 1 {
            println!("{}", 1);
        } else {
            println!("{}", b - 2);
        }
    } else {
        let ans = n * m - (2 * n + 2 * m - 4);
        println!("{}", ans);
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, VecDeque};

pub trait FromLn {
    fn fromln(s: &str) -> Self;
}
pub fn readln<T: FromLn>() -> T {
    let mut buf = String::new();
    let _ = ::std::io::stdin().read_line(&mut buf).unwrap();
    T::fromln(buf.trim())
}
pub fn readlns<T: FromLn>(n: usize) -> Vec<T> {
    let mut vs = vec![];
    for _ in 0..n {
        vs.push(readln());
    }
    vs
}
macro_rules! fromln_primitives {
    ($($t:ty),*) => { $(
        impl FromLn for $t {
            fn fromln(s: &str) -> $t {
                s.parse().unwrap()
            }
        }
    )* }
}
fromln_primitives!(
    String,
    bool,
    f32,
    f64,
    isize,
    i8,
    i16,
    i32,
    i64,
    usize,
    u8,
    u16,
    u32,
    u64
);
impl<T> FromLn for Vec<T>
where
    T: FromLn,
{
    fn fromln(s: &str) -> Vec<T> {
        s.split_whitespace().map(T::fromln).collect()
    }
}
impl FromLn for Vec<char> {
    fn fromln(s: &str) -> Vec<char> {
        s.chars().collect()
    }
}
macro_rules! fromln_tuple {
    ($($t:ident),*) => {
        impl<$($t),*> FromLn for ($($t),*) where $($t: FromLn),* {
            fn fromln(s: &str) -> ($($t),*) {
                let mut it = s.split_whitespace();
                let t = ($($t::fromln(it.next().unwrap())),*);
                assert_eq!(it.next(), None);
                t
            }
        }
    }
}
fromln_tuple!(A, B);
fromln_tuple!(A, B, C);
fromln_tuple!(A, B, C, D);
fromln_tuple!(A, B, C, D, E);
fromln_tuple!(A, B, C, D, E, F);
mod comp {
    pub mod math {
        pub mod comb {
            use super::mint::{Mint, MOD};
            pub struct Comb {
                fact: Vec<Mint>,
                factinv: Vec<Mint>,
            }
            impl Comb {}
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let c = Comb::new(100);
                    assert_eq!(Mint::from(336), c.perm(8, 3));
                    assert_eq!(Mint::from(56), c.comb(8, 3));
                    assert_eq!(Mint::from(10), c.multi_comb(3, 3));
                }
                #[test]
                fn test_fact() {
                    let c = Comb::new(100);
                    let p = 8721234;
                    let mut f = Mint::from(1);
                    for i in 1..(p + 1) {
                        f *= i;
                    }
                    assert_eq!(f, c.fact(p));
                }
            }
        }
        pub mod mint {
            use std;
            pub const MOD: u32 = 1000000007;
            #[derive(Debug, Copy, Clone, Eq)]
            pub struct Mint {
                val: u32,
            }
            impl<T: Into<Mint>> std::ops::Add<T> for Mint {
                type Output = Mint;
                fn add(self, other: T) -> Mint {
                    let nval = self.val + other.into().val;
                    Mint {
                        val: if nval >= MOD { nval - MOD } else { nval },
                    }
                }
            }
            impl<T: Into<Mint>> std::ops::Sub<T> for Mint {
                type Output = Mint;
                fn sub(self, other: T) -> Mint {
                    let nval = self.val + MOD - other.into().val;
                    Mint {
                        val: if nval >= MOD { nval - MOD } else { nval },
                    }
                }
            }
            impl<T: Into<Mint>> std::ops::Mul<T> for Mint {
                type Output = Mint;
                fn mul(self, other: T) -> Mint {
                    let nval = self.val as u64 * other.into().val as u64;
                    Mint {
                        val: (nval % (MOD as u64)) as u32,
                    }
                }
            }
            impl<T: Into<Mint>> std::ops::Div<T> for Mint {
                type Output = Mint;
                fn div(self, other: T) -> Mint {
                    self * other.into().inv()
                }
            }
            impl Mint {
                pub fn inv(self) -> Mint {
                    let mut a = self.val as i32;
                    let mut b = MOD as i32;
                    let mut u = 1 as i32;
                    let mut v = 0 as i32;
                    while b != 0 {
                        let t = a / b;
                        a -= t * b;
                        std::mem::swap(&mut a, &mut b);
                        u -= t * v;
                        std::mem::swap(&mut u, &mut v);
                    }
                    Mint {
                        val: if u < 0 { u + MOD as i32 } else { u } as u32,
                    }
                }
            }
            impl PartialEq for Mint {
                fn eq(&self, other: &Mint) -> bool {
                    self.val == other.val
                }
            }
            impl std::fmt::Display for Mint {
                fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
                    self.val.fmt(f)
                }
            }
            macro_rules! impl_signed_mint(( $ ( $ t : ty ) * ) => (
                                      $ (
                                      impl From < $ t > for Mint {
                                      # [ inline ] fn from ( x : $ t ) -> Mint
                                      {
                                      let t = ( x as i64 ) % ( MOD as i64 ) ;
                                      if x >= 0 { Mint { val : t as u32 } }
                                      else {
                                      Mint { val : ( MOD as i64 + t ) as u32 }
                                      } } } ) * ));
            macro_rules! impl_unsigned_mint(( $ ( $ t : ty ) * ) => (
                                        $ (
                                        impl From < $ t > for Mint {
                                        # [ inline ] fn from ( x : $ t ) ->
                                        Mint {
                                        let t = x as u64 % MOD as u64 ; Mint {
                                        val : t as u32 } } } ) * ));
            impl_signed_mint! (i8 i16 i32 i64 isize);
            impl_unsigned_mint! (u8 u16 u32 u64 usize);
            impl<T: Into<Mint>> std::ops::AddAssign<T> for Mint {
                fn add_assign(&mut self, other: T) {
                    *self = *self + other.into();
                }
            }
            impl<T: Into<Mint>> std::ops::SubAssign<T> for Mint {
                fn sub_assign(&mut self, other: T) {
                    *self = *self - other.into();
                }
            }
            impl<T: Into<Mint>> std::ops::MulAssign<T> for Mint {
                fn mul_assign(&mut self, other: T) {
                    *self = *self * other.into();
                }
            }
            impl<T: Into<Mint>> std::ops::DivAssign<T> for Mint {
                fn div_assign(&mut self, other: T) {
                    *self = *self / other.into();
                }
            }
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let a: Mint = Mint::from(3);
                    let b: Mint = Mint::from(1000000000);
                    assert_eq!(Mint::from(3000000000u64 % MOD as u64), a * b);
                }
            }
        }
        pub mod prime {
            #[derive(Copy, Clone, PartialEq, PartialOrd, Ord, Eq, Debug)]
            struct U128 {
                hi: u64,
                lo: u64,
            }
        }
    }
    pub mod data_structure {
        pub mod bit {
            pub struct BIT {
                tree: Vec<i64>,
            }
            pub struct BITRange {
                bit0: BIT,
                bit1: BIT,
            }
            impl BIT {}
            impl BITRange {}
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let mut bit = BIT::new(10);
                    bit.add(2, 1);
                    bit.add(3, 3);
                    bit.add(5, 10);
                    bit.add(0, -4);
                    bit.add(9, -5);
                    assert_eq!(5, bit.get(0, 10));
                    assert_eq!(4, bit.get(2, 4));
                    assert_eq!(1, bit.get(2, 3));
                    assert_eq!(0, bit.get(2, 2));
                    assert_eq!(0, bit.get(2, 0));
                    assert_eq!(-4, bit.get(0, 1));
                    assert_eq!(5, bit.get(5, 10));
                    let mut bit = BITRange::new(10);
                    bit.add(1, 3, 1);
                    bit.add(2, 5, 2);
                    assert_eq!(1, bit.get(1, 2));
                    assert_eq!(4, bit.get(1, 3));
                    assert_eq!(6, bit.get(1, 4));
                    assert_eq!(6, bit.get(0, 4));
                }
            }
        }
        pub mod union_find {
            pub struct UnionFind {
                data: Vec<i32>,
            }
            impl UnionFind {}
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let mut uf = UnionFind::new(3);
                    assert_eq!(1, uf.size(0));
                    assert_eq!(1, uf.size(1));
                    assert_eq!(1, uf.size(2));
                    assert_eq!(0, uf.root(0));
                    assert_eq!(1, uf.root(1));
                    assert_eq!(2, uf.root(2));
                    assert!(!uf.same(1, 2));
                    uf.unite(1, 2);
                    assert_ne!(uf.root(0), uf.root(2));
                    assert_eq!(uf.root(1), uf.root(2));
                    assert_eq!(1, uf.size(0));
                    assert_eq!(2, uf.size(1));
                    assert_eq!(2, uf.size(2));
                    assert!(uf.same(1, 2));
                    uf.unite(0, 1);
                    assert_eq!(uf.root(0), uf.root(2));
                    assert_eq!(uf.root(1), uf.root(2));
                    assert_eq!(3, uf.size(0));
                    assert_eq!(3, uf.size(1));
                    assert_eq!(3, uf.size(2));
                    assert!(uf.same(1, 2));
                    assert!(uf.same(0, 2));
                }
            }
        }
    }
    pub mod util {
        pub mod permutation {
            pub trait Permutation {
                fn next_permutation(&mut self) -> bool;
                fn prev_permutation(&mut self) -> bool;
            }
            impl<T> Permutation for [T]
            where
                T: Ord,
            {
                fn next_permutation(&mut self) -> bool {
                    if self.len() <= 1 {
                        return false;
                    }
                    let mut i = self.len() - 1;
                    while i > 0 && self[i - 1] >= self[i] {
                        i -= 1;
                    }
                    if i == 0 {
                        return false;
                    }
                    let mut j = self.len() - 1;
                    while self[j] <= self[i - 1] {
                        j -= 1;
                    }
                    self.swap(j, i - 1);
                    self[i..].reverse();
                    true
                }
                fn prev_permutation(&mut self) -> bool {
                    if self.len() <= 1 {
                        return false;
                    }
                    let mut i = self.len() - 1;
                    while i > 0 && self[i - 1] <= self[i] {
                        i -= 1;
                    }
                    if i == 0 {
                        return false;
                    }
                    self[i..].reverse();
                    let mut j = self.len() - 1;
                    while self[j - 1] < self[i - 1] {
                        j -= 1;
                    }
                    self.swap(i - 1, j);
                    true
                }
            }
            #[cfg(test)]
            mod tests {
                use super::*;
                #[test]
                fn test_simple() {
                    let mut data = [0, 0, 1, 1, 2];
                    data.next_permutation();
                    assert_eq!(&data, &[0, 0, 1, 2, 1]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 0, 2, 1, 1]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 1, 0, 1, 2]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 1, 0, 2, 1]);
                    data.next_permutation();
                    assert_eq!(&data, &[0, 1, 1, 0, 2]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 1, 0, 2, 1]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 1, 0, 1, 2]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 0, 2, 1, 1]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 0, 1, 2, 1]);
                    data.prev_permutation();
                    assert_eq!(&data, &[0, 0, 1, 1, 2]);
                    assert!(!data.prev_permutation());
                }
            }
        }
        pub mod rand {
            use std::{marker, mem};
            use std::io::{self, Read};
            use std::fs::File;
            use std::char;
            #[derive(Debug, Clone, Copy)]
            pub struct Xoroshiro128Rng {
                state: [u64; 2],
            }
            impl Xoroshiro128Rng {}
            impl Rng for Xoroshiro128Rng {
                fn next_u32(&mut self) -> u32 {
                    self.next_u64() as u32
                }
                fn next_u64(&mut self) -> u64 {
                    let s0: u64 = self.state[0];
                    let mut s1: u64 = self.state[1];
                    let result: u64 = s0.wrapping_add(s1);
                    s1 ^= s0;
                    self.state[0] = s0.rotate_left(55) ^ s1 ^ (s1 << 14);
                    self.state[1] = s1.rotate_left(36);
                    result
                }
            }
            pub trait Rand: Sized {
                fn rand<R: Rng>(rng: &mut R) -> Self;
            }
            pub trait Rng {
                fn next_u32(&mut self) -> u32;
                fn next_u64(&mut self) -> u64 {
                    let x = self.next_u32() as u64;
                    let y = self.next_u32() as u64;
                    (y << 32) | x
                }
                fn next_f32(&mut self) -> f32 {
                    const UPPER_MASK: u32 = 1065353216;
                    const LOWER_MASK: u32 = 8388607;
                    let tmp = UPPER_MASK | (self.next_u32() & LOWER_MASK);
                    let result: f32 = unsafe { mem::transmute(tmp) };
                    result - 1.0
                }
                fn next_f64(&mut self) -> f64 {
                    const UPPER_MASK: u64 = 4607182418800017408;
                    const LOWER_MASK: u64 = 4503599627370495;
                    let tmp = UPPER_MASK | (self.next_u64() & LOWER_MASK);
                    let result: f64 = unsafe { mem::transmute(tmp) };
                    result - 1.0
                }
                #[inline(always)]
                fn gen<T: Rand>(&mut self) -> T
                where
                    Self: Sized,
                {
                    Rand::rand(self)
                }
                fn gen_iter<'a, T: Rand>(&'a mut self) -> Generator<'a, T, Self>
                where
                    Self: Sized,
                {
                    Generator {
                        rng: self,
                        _marker: marker::PhantomData,
                    }
                }
                fn shuffle<T>(&mut self, values: &mut [T])
                where
                    Self: Sized,
                {
                    let mut i = values.len();
                    while i >= 2 {
                        i -= 1;
                        values.swap(i, (self.next_u64() as usize) % i);
                    }
                }
            }
            #[derive(Debug)]
            pub struct Generator<'a, T, R: 'a> {
                rng: &'a mut R,
                _marker: marker::PhantomData<fn() -> T>,
            }
            impl<'a, T: Rand, R: Rng> Iterator for Generator<'a, T, R> {
                type Item = T;
                fn next(&mut self) -> Option<T> {
                    Some(self.rng.gen())
                }
            }
            pub struct OsRng {
                reader: File,
            }
            impl OsRng {}
            impl Rng for OsRng {
                fn next_u32(&mut self) -> u32 {
                    let mut dest = [0u8; 4];
                    self.reader.read_exact(&mut dest).unwrap();
                    unsafe { mem::transmute::<[u8; 4], u32>(dest) }
                }
            }
            impl Rand for isize {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> isize {
                    if mem::size_of::<isize>() == 4 {
                        rng.gen::<i32>() as isize
                    } else {
                        rng.gen::<i64>() as isize
                    }
                }
            }
            impl Rand for i8 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i8 {
                    rng.next_u32() as i8
                }
            }
            impl Rand for i16 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i16 {
                    rng.next_u32() as i16
                }
            }
            impl Rand for i32 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i32 {
                    rng.next_u32() as i32
                }
            }
            impl Rand for i64 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i64 {
                    rng.next_u64() as i64
                }
            }
            #[cfg(feature = "i128_support")]
            impl Rand for i128 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> i128 {
                    rng.gen::<u128>() as i128
                }
            }
            impl Rand for usize {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> usize {
                    if mem::size_of::<usize>() == 4 {
                        rng.gen::<u32>() as usize
                    } else {
                        rng.gen::<u64>() as usize
                    }
                }
            }
            impl Rand for u8 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u8 {
                    rng.next_u32() as u8
                }
            }
            impl Rand for u16 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u16 {
                    rng.next_u32() as u16
                }
            }
            impl Rand for u32 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u32 {
                    rng.next_u32()
                }
            }
            impl Rand for u64 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u64 {
                    rng.next_u64()
                }
            }
            #[cfg(feature = "i128_support")]
            impl Rand for u128 {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> u128 {
                    ((rng.next_u64() as u128) << 64) | (rng.next_u64() as u128)
                }
            }
            impl Rand for f64 {
                fn rand<R: Rng>(rng: &mut R) -> f64 {
                    rng.next_f64()
                }
            }
            impl Rand for f32 {
                fn rand<R: Rng>(rng: &mut R) -> f32 {
                    rng.next_f32()
                }
            }
            impl Rand for char {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> char {
                    const CHAR_MASK: u32 = 2097151;
                    loop {
                        match char::from_u32(rng.next_u32() & CHAR_MASK) {
                            Some(c) => return c,
                            None => {}
                        }
                    }
                }
            }
            impl Rand for bool {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> bool {
                    rng.gen::<u8>() & 1 == 1
                }
            }
            macro_rules! tuple_impl(( $ ( $ tyvar : ident ) , * ) => {
                                impl < $ ( $ tyvar : Rand ) , * > Rand for (
                                $ ( $ tyvar ) , * , ) {
                                # [ inline ] fn rand < R : Rng > (
                                _rng : & mut R ) -> ( $ ( $ tyvar ) , * , ) {
                                ( $ ( _rng . gen :: < $ tyvar > (  ) ) , * , )
                                } } });
            impl Rand for () {
                #[inline]
                fn rand<R: Rng>(_: &mut R) -> () {
                    ()
                }
            }
            tuple_impl!(A);
            tuple_impl!(A, B);
            tuple_impl!(A, B, C);
            tuple_impl!(A, B, C, D);
            tuple_impl!(A, B, C, D, E);
            tuple_impl!(A, B, C, D, E, F);
            tuple_impl!(A, B, C, D, E, F, G);
            tuple_impl!(A, B, C, D, E, F, G, H);
            tuple_impl!(A, B, C, D, E, F, G, H, I);
            tuple_impl!(A, B, C, D, E, F, G, H, I, J);
            tuple_impl!(A, B, C, D, E, F, G, H, I, J, K);
            tuple_impl!(A, B, C, D, E, F, G, H, I, J, K, L);
            macro_rules! array_impl({
                                $ n : expr , $ t : ident , $ ( $ ts : ident ,
                                ) * } => {
                                array_impl ! { ( $ n - 1 ) , $ ( $ ts , ) * }
                                impl < T > Rand for [ T ; $ n ] where T : Rand
                                {
                                # [ inline ] fn rand < R : Rng > (
                                _rng : & mut R ) -> [ T ; $ n ] {
                                [
                                _rng . gen :: < $ t > (  ) , $ (
                                _rng . gen :: < $ ts > (  ) ) , * ] } } } ; {
                                $ n : expr , } => {
                                impl < T > Rand for [ T ; $ n ] {
                                fn rand < R : Rng > ( _rng : & mut R ) -> [
                                T ; $ n ] { [  ] } } } ;);
            array_impl!(
                32,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
                T,
            );
            impl<T: Rand> Rand for Option<T> {
                #[inline]
                fn rand<R: Rng>(rng: &mut R) -> Option<T> {
                    if rng.gen() {
                        Some(rng.gen())
                    } else {
                        None
                    }
                }
            }
        }
    }
}