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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define FOR(i,start,end) for(int i=start;i<=end;i++)
const int INF = 1001001001;
typedef long long ll;
const ll MOD=1000000007;
using namespace std;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<class T>auto MAX(const T& a) { return *max_element(a.begin(),a.end()); }
template<class T>auto MIN(const T& a) { return *min_element(a.begin(),a.end()); }
template<class T, class U>U SUM(const T& a, const U& v) { return accumulate(a.begin(),a.end(), v); }
template<class T, class U>U COUNT(const T& a, const U& v) { return count(a.begin(),a.end(), v); }
template<class T, class U>int LOWER(const T& a, const U& v) { return lower_bound(a.begin(),a.end(), v) - a.begin(); }
template<class T, class U>int UPPER(const T& a, const U& v) { return upper_bound(a.begin(),a.end(), v) - a.begin(); }
int GCD(int a, int b) { return b ? GCD(b, a%b) : a; }
int LCM(int a, int b) { int g = GCD(a, b); return a / g * b; }
//---------------------------------------------------------------------------------------------------
template<int MOD> struct ModInt {
    static const int Mod = MOD; unsigned x; ModInt() : x(0) { }
    ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; }
    int get() const { return (int)x; }
    ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
    ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
    ModInt &operator/=(ModInt that) { return *this *= that.inverse(); }
    ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
    ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
    ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
    ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
    ModInt inverse() const { long long a = x, b = MOD, u = 1, v = 0;
        while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); }
        return ModInt(u); }
    bool operator==(ModInt that) const { return x == that.x; }
    bool operator!=(ModInt that) const { return x != that.x; }
    ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ostream& operator<<(ostream& st, const ModInt<MOD> a) { st << a.get(); return st; };
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
    ModInt<MOD> r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; }
template<typename T, int FAC_MAX> struct Comb { vector<T> fac, ifac;
    Comb(){fac.resize(FAC_MAX,1);ifac.resize(FAC_MAX,1);FOR(i,1,FAC_MAX-1)fac[i]=fac[i-1]*i;
        ifac[FAC_MAX-1]=T(1)/fac[FAC_MAX-1];for(int i=FAC_MAX-2;i>=1;i--)ifac[i]=ifac[i+1]*T(i+1);}
    T aPb(int a, int b) { if (b < 0 || a < b) return T(0); return fac[a] * ifac[a - b]; }
    T aCb(int a, int b) { if (b < 0 || a < b) return T(0); return fac[a] * ifac[a - b] * ifac[b]; }
    T nHk(int n, int k) { if (n == 0 && k == 0) return T(1); if (n <= 0 || k < 0) return 0;
        return aCb(n + k - 1, k); } // nHk = (n+k-1)Ck : n is separator
    T pairCombination(int n) {if(n%2==1)return T(0);return fac[n]*ifac[n/2]/(T(2)^(n/2));}
    // combination of paris for n
}; 
typedef ModInt<1000000007> mint;
bool isPrime(int x){
    int i;
    if(x < 2)return 0;
    else if(x == 2) return 1;
    if(x%2 == 0) return 0;
    for(i = 3; i*i <= x; i += 2) if(x%i == 0) return 0;
    return 1;
}

int main(void){
    // Your code here!
    ll n,ans = 2;
    cin >> n;
    bool flag = true;
    vector<int> A(n/2+1,0);

    rep(i,n) {
        int a; cin >> a;
        if (n % 2 == 0) {
            if ( a % 2 == 0) {
                flag = false;
            }
        } else {
            if (a % 2 == 1) {
                flag = false;
            }
        }

        A[a/2]++;
    }
    
    if ( n % 2 == 1) {
        FOR(i,1,n/2) {
            if(A[0] !=1 || A[i] != 2) {
                flag = false;
            }
        }
    } else {
        rep(i,n/2) {
            if(A[i] != 2) {
                flag = false;
            }
        }
    }

    rep(i,n/2-1) {
        ans *= 2;
        ans %= MOD;
    }

    if (flag) {
        if(n == 1) {
            cout << 1 << endl;
        } else {
            cout << ans << endl;
        }
    } else {
        cout << 0 << endl;
    }
}
// 基本的にはlong long を使いましょう