Problem:
Score : 300 points

Problem Statement

There are N people, conveniently numbered 1 through N.
They were standing in a row yesterday, but now they are unsure of the order in which they were standing.
However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.
According to their reports, the difference above for person i is A_i.

Based on these reports, find the number of the possible orders in which they were standing.
Since it can be extremely large, print the answer modulo 10^9+7.
Note that the reports may be incorrect and thus there may be no consistent order.
In such a case, print 0.

Constraints

1≦N≦10^5

0≦A_i≦N-1

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the number of the possible orders in which they were standing, modulo 10^9+7.

Sample Input 1

5
2 4 4 0 2

Sample Output 1

4

There are four possible orders, as follows:

2,1,4,5,3

2,5,4,1,3

3,1,4,5,2

3,5,4,1,2

Sample Input 2

7
6 4 0 2 4 0 2

Sample Output 2

0

Any order would be inconsistent with the reports, thus the answer is 0.

Sample Input 3

8
7 5 1 1 7 3 5 3

Sample Output 3

16

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

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};
type Num = usize;
const MOD: Num = 1_000_000_007;
#[derive(Clone, Copy)]
pub struct ModInt<T: Copy + Clone>(T);
impl ModInt<Num> {
    pub fn value(self) -> Num {
        self.0
    }
    pub fn pow(self, e: usize) -> ModInt<Num> {
        let mut result = ModInt(1);
        let mut cur = self;
        let mut e = e;
        while e > 0 {
            if e & 1 == 1 {
                result *= cur;
            }
            e >>= 1;
            cur *= cur;
        }
        result
    }
}
impl Add<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD
        }
        let mut t = rhs + self.0;
        if t >= MOD {
            t -= MOD
        }
        ModInt(t)
    }
}
impl Add<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self + rhs.0
    }
}
impl AddAssign<Num> for ModInt<Num> {
    fn add_assign(&mut self, other: Num) {
        *self = *self + other;
    }
}
impl AddAssign<ModInt<Num>> for ModInt<Num> {
    fn add_assign(&mut self, other: ModInt<Num>) {
        *self = *self + other;
    }
}
impl Sub<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD
        }
        let value = if self.0 < rhs {
            self.0 + MOD - rhs
        } else {
            self.0 - rhs
        };
        ModInt(value)
    }
}
impl Sub<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self - rhs.0
    }
}
impl SubAssign<Num> for ModInt<Num> {
    fn sub_assign(&mut self, other: Num) {
        *self = *self - other;
    }
}
impl SubAssign<ModInt<Num>> for ModInt<Num> {
    fn sub_assign(&mut self, other: ModInt<Num>) {
        *self = *self - other;
    }
}
impl Mul<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn mul(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD
        }
        let t = (self.0 * rhs) % MOD;
        ModInt(t)
    }
}
impl Mul<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn mul(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self * rhs.0
    }
}
impl MulAssign<Num> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: Num) {
        *self = *self * rhs;
    }
}
impl MulAssign<ModInt<Num>> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self * rhs;
    }
}
impl Div<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, mut rhs: Num) -> ModInt<Num> {
        if rhs >= MOD {
            rhs %= MOD
        }
        self * ModInt(rhs).pow(MOD - 2)
    }
}
impl Div<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self / rhs.0
    }
}
impl DivAssign<Num> for ModInt<Num> {
    fn div_assign(&mut self, rhs: Num) {
        *self = *self / rhs
    }
}
impl DivAssign<ModInt<Num>> for ModInt<Num> {
    fn div_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self / rhs
    }
}

fn main() {
    input! {
        n: usize,
        a: [u32;n]
    }
    let mut a = a;
    a.sort();
    if n % 2 == 0 {
        let mut i = 0;
        let mut k = 1;
        while i < n {
            if k != a[i] || k != a[i+1] {
                println!("{}", 0);
                return;
            }
            i += 2;
            k += 2;
        }
        println!("{}", ModInt(2).pow(n / 2).value());
    } else {
        if a[0] != 0 {
            println!("{}", 0);
            return;
        }
        let mut i = 1;
        let mut k = 2;
        while i < n {
            if k != a[i] || k != a[i+1] {
                println!("{}", 0);
                return;
            }
            i += 2;
            k += 2;
        }
        println!("{}", ModInt(2).pow((n-1) / 2).value());
    }
}