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>
using namespace std;

#define int long long
struct Fast {Fast(){std::cin.tie(0);ios::sync_with_stdio(false);}} fast;

/* short */
#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define ALL(v) begin(v), end(v)

/* REPmacro */
#define FOR(i, s, n) for (int i = (s); i < (n); i++)
#define RFOR(i, s, n) for (int i = (s); i >= (n); i--)
#define rep(i, n) FOR(i, 0, n)
#define repi(i, n) FOR(i, 1, n + 1)
#define rrep(i, n) RFOR(i, n - 1, 0)
#define rrepi(i, n) RFOR(i, n, 1)

/* debug */
#define pp(v) cerr << #v "=" << (v) << endl;

/* alias */
using ll = long long;
using ull = unsigned long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using pii = pair<int, int>;
using mii = map<int, int>;
using vs = vector<string>;
using Graph = vvi;
template <typename T> using PQ = priority_queue<T>;
template <typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;

/* iostream */
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }

/* const */
const int INF = 1001001001;
const ll LINF = 1001001001001001001ll;
const int MOD = 1e9 + 7;
const int dx[] = {0, 1, 0, -1, 1, -1, 1, -1}, dy[] = {1, 0, -1, 0, 1, -1, -1, 1};

/* func */
#define UNIQUE(v) v.erase( unique(ALL(v)), v.end() );
#define TIME system("date +%M:%S.%N")
inline bool inside(int y, int x, int H, int W) {return y >= 0 && x >= 0 && y < H && x < W;}
template <typename T> inline bool chmin(T& a, const T& b) {if (a > b) a = b; return a > b;}
template <typename T> inline bool chmax(T& a, const T& b) {if (a < b) a = b; return a < b;}
template<class T> T gcd(const T &a, const T &b) { return a < b ? gcd(b, a) : b ? gcd(b, a % b) : a; }
template<class T> T lcm(const T &a, const T &b) { return a / gcd(a, b) * b; }
template<class T> T div_ceil(const T &a, const T &b) { return (a + b - 1) / b; }

int solve(mii &c, int m, int n) {
  for (auto v : c) {
    if (v.fst % 2 != m) return 0;
    if (v.snd != 2 && v.fst != 0) return 0;
    if (v.snd != 1 && v.fst == 0) return 0;
  }
  int ans = 1;
  rep(i,n/2) ans = ans * 2 % MOD;
  return ans;
}

signed main() {
  int n;cin>>n;
  vi a(n);cin>>a;
  mii c;rep(i,n) c[a[i]]++;
  int m = a[0]%2;
  int ans = solve(c,m,n);
  cout << ans << endl;
}