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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;
namespace AtCoder {
    class MainClass {
        //C#7.0/////////////////////////////////////////////////////
        int N;
        long[] A;
        void Solve() {
            io.i(out N);
            io.ini(out A, N);

            long ans = 0;
            var mustHave = new List<long>();
            for(int i = 0; (N-1)-2*i > 0; i++) 
                mustHave.Add((N - 1) - 2 * i);

            var aa = new AssociativeArray<long>(A);

            if(!aa.allContainsK(mustHave.ToArray())||aa.Val(0)>=2)
                goto EXIT;

            int mod = (int)1e+9;
            ans = 1;
            foreach(var kp in aa.dic) {
                ans *= kp.Value;
                ans %= mod;
            }

            EXIT:;
            io.o(ans);

        }

        ////////////////////////////////////////////////////////////
        public static void Main(string[] args) { new MainClass().Stream(); }
        IO io = new IO();
        void Stream() { Solve(); io.writeFlush(); }
        //void Stream() { Test(); io.writeFlush(); }
        void Test() { }
        #region MockMacro
        //Hack Update
        //cannot use break,continue,goto
        void FOR(int a, int b, Action<int> act, int c = 1) { for (int i = a; i < b; i += c) act(i); }
        void FOR(int a, int b, Action<int> act, Func<int, bool> con, int c = 1) { for (int i = a; i < b && con(i); i += c) act(i); }
        void RFOR(int a, int b, Action<int> act, int c = 1) { for (int i = a; i >= b; i -= c) act(i); }
        void RFOR(int a, int b, Action<int> act, Func<int, bool> con, int c = 1) { for (int i = a; i >= b && con(i); i -= c) act(i); }
        void REP(int n, Action<int> act, Func<int, bool> con, int c = 1) { for (int i = 0; i < n && con(i); i += c) act(i); }
        void REP(int n, Action<int> act, int c = 1) { for (int i = 0; i < n; i += c) act(i); }
        void RREP(int n, Action<int> act, int c = 1) { for (int i = n - 1; i >= 0; i -= c) act(i); }
        void RREP(int n, Action<int> act, Func<int, bool> con) { for (int i = n - 1; i >= 0 && con(i); i--) act(i); }
        #endregion
    }
    #region default
    class IO {
        string[] nextBuffer; int BufferCnt; char[] cs = new char[] { ' ' };
        StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        public IO() { nextBuffer = new string[0]; BufferCnt = 0; Console.SetOut(sw); }
        public string Next() {
            if (BufferCnt < nextBuffer.Length) return nextBuffer[BufferCnt++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            BufferCnt = 0;
            return nextBuffer[BufferCnt++];
        }
        public string next => Next();
        public char nextChar => char.Parse(next);
        public int nextInt => int.Parse(next);
        public long nextLong => long.Parse(next);
        public double nextDouble => double.Parse(next);
        public string[] arr => Console.ReadLine().Split(' ');
        public char[] arrChar => Array.ConvertAll(arr, char.Parse);
        public int[] arrInt => Array.ConvertAll(arr, int.Parse);
        public long[] arrLong => Array.ConvertAll(arr, long.Parse);
        public double[] arrDouble => Array.ConvertAll(arr, double.Parse);
        private bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
        private T convertType<T, U>(U v) { return (T)Convert.ChangeType(v, typeof(T)); }
        private T suitType<T>(string s) {
            if (typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
            if (typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
            if (typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
            if (typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
            return convertType<T, string>(s);
        }
        public void i<T>(out T v) { v = suitType<T>(next); }
        public void i<T, U>(out T v1, out U v2) { i(out v1); i(out v2); }
        public void i<T, U, V>(out T v1, out U v2, out V v3) {
            i(out v1); i(out v2); i(out v3);
        }
        public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4) {
            i(out v1); i(out v2); i(out v3); i(out v4);
        }
        public void i<T, U, V, W, X>(out T v1, out U v2, out V v3, out W v4, out X v5) {
            i(out v1); i(out v2); i(out v3); i(out v4); i(out v5);
        }
        public void ini(out int[] a, int size) {
            a = new int[size]; for (int i = 0; i < size; i++) a[i] = nextInt;
        }
        public void ini(out long[] a, int size) {
            a = new long[size]; for (int i = 0; i < size; i++) a[i] = nextLong;
        }
        public void ini(out int[] a1, out int[] a2, int size) {
            a1 = new int[size]; a2 = new int[size];
            for (int i = 0; i < size; i++) { a1[i] = nextInt; a2[i] = nextInt; }
        }
        public void ini(out long[] a1, out long[] a2, int size) {
            a1 = new long[size]; a2 = new long[size];
            for (int i = 0; i < size; i++) { a1[i] = nextLong; a2[i] = nextLong; }
        }
        public void ini(out int[,] g, int h, int w) {
            g = new int[h, w]; for (int i = 0; i < h; i++)
                for (int j = 0; j < w; j++) g[i, j] = nextInt;
        }
        public void ini(out string[] a, int size) {
            a = new string[size]; for (int i = 0; i < size; i++) a[i] = next;
        }
        public void inii(out int[] a, int size) {
            a = new int[size]; for (int i = 0; i < size; i++) a[i] = nextInt - 1;
        }
        public void inii(out int[] a1, out int[] a2, int size) {
            a1 = new int[size]; a2 = new int[size];
            for (int i = 0; i < size; i++) { a1[i] = nextInt - 1; a2[i] = nextInt - 1; }
        }
        public void inii(out int[,] a, int size) {
            a = new int[size, size]; for (int i = 0; i < size; i++)
                for (int j = 0; j < size; j++) a[i, j] = nextInt - 1;
        }
        public void o<T>(T v) { Console.WriteLine(v); }
        public void ol<T>(T v) { Console.Write(v + " "); }
        public void o<T>(params T[] a) { foreach (T v in a) o(v); }
        public void o<T>(List<T> l) { o(l.ToArray()); }
        public void ol<T>(params T[] a) { foreach (T v in a) { ol(v); } br(); }
        public void ol<T>(List<T> l) { ol(l.ToArray()); }
        public void YN(bool f) { o(f ? "YES" : "NO"); }
        public void Yn(bool f) { o(f ? "Yes" : "No"); }
        public void yn(bool f) { o(f ? "yes" : "no"); }
        public void br() { o(""); }
        public void writeFlush() { Console.Out.Flush(); }
    }
    #endregion
    #region other
    class Mat {
        public int mod = 1000000007;//10^9+7
        public long Pow(long a, long b) {
            if (b == 0) return 1;
            if (b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n) {
            return (n != 0) ? (n % mod * (Fact(n - 1) % mod) % mod) : 1;
        }
        public long C(long n, long r) {
            if (r == 0 || n == r) return 1;
            else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public long Sum(params long[] a) {
            return a.Aggregate((v, next) => (v % mod + next) % mod);
        }
        public int GCD(int a, int b) {
            if (a < b) Swap(ref a, ref b); return b == 0 ? a : GCD(b, a % b);
        }
        public int GCD(int[] array) { return array.Aggregate((v, next) => GCD(v, next)); }
        public bool isPrime(long n) {
            if (n == 2) return true; if (n < 2 || n % 2 == 0) return false;
            for (long v = 3; v <= (long)Math.Sqrt(n); v += 2) if (n % v == 0) return false;
            return true;
        }
        public void Swap<T>(ref T a, ref T b) { T tmp = a; a = b; b = tmp; }
        public T Max<T>(params T[] v) { return v.Max(); }
        public T Min<T>(params T[] v) { return v.Min(); }
        public double Dis(int x1, int y1, int x2, int y2) { return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2)); }
        public int mDis(int x1, int y1, int x2, int y2) { return Math.Abs(x1 - x2) + Math.Abs(y1 - y2); }
        public int Digit(long n) { return (n == 0) ? 1 : (int)Math.Log10(n) + 1; }
        //test
        public int DigitValue(int n, int dig) { return (n % (int)Pow(10, dig)) / (int)Pow(10, dig - 1); }
        /*
        public int[] DigVal(int n) {//桁の順番...
            int[] ret = new int[Digit(n)];
            return ret;
        }
        */
        //
        public int Clamp(int n, int a, int b) { return (n < a) ? a : (b < n) ? b : n; }
        public long Clamp(long n, long a, long b) { return (n < a) ? a : (b < n) ? b : n; }
        public double Clamp(double n, double a, double b) { return (n < a) ? a : (b < n) ? b : n; }
        public long Tousa(long a, long d, int n) { return a + (n - 1) * d; }
        public long TousaSum(long a, long d, int n) { return n * (2 * a + (n - 1) * d) / 2; }
    }
    class AssociativeArray<T> {
        public Dictionary<T, int> dic;
        public AssociativeArray() { dic = new Dictionary<T, int>(); }
        public AssociativeArray(params T[] a) { dic = new Dictionary<T, int>(); Add(a); }
        public void Add(params T[] a) {
            for (int i = 0; i < a.Length; i++) {
                if (!dic.ContainsKey(a[i])) dic[a[i]] = 0; dic[a[i]]++;
            }
        }
        public T[] Keys() { return dic.Keys.ToArray<T>(); }
        public int Val(T k) { return (dic.ContainsKey(k)) ? dic[k] : 0; }
        public int ValueSum() { return dic.Values.Sum(); }
        public int KeyNum() { return dic.Keys.Count; }
        public int MaxVal() { return dic.Values.Max(); }
        public int MinVal() { return dic.Values.Min(); }
        public T MaxKey() { return dic.First(d => d.Value == MaxVal()).Key; }
        public T MinKey() { return dic.First(d => d.Value == MinVal()).Key; }
        public bool isContainsK(T k) { return dic.ContainsKey(k); }
        public bool anyContainsK(params T[] k) { return k.Any(key => isContainsK(key)); }
        public bool allContainsK(params T[] k) { return k.All(key => isContainsK(key)); }
        public void Show() { foreach (var v in dic) { Console.WriteLine(v.Key + " : " + v.Value); } }
        //:sort->array
    }
    class WarshallFloyd {
        int INF;
        public WarshallFloyd() { INF = (int)(1e8); }
        public WarshallFloyd(int INF) { this.INF = INF; }
        public int[,] Run(int[,] m) {
            int edgeLength = m.GetLength(0);
            for (int i = 0; i < edgeLength; i++)
                for (int j = 0; j < edgeLength; j++)
                    for (int k = 0; k < edgeLength; k++)
                        m[j, k] = Math.Min(m[j, k], m[j, i] + m[i, k]);
            return m;
        }
        public int[,] Init(int n) {
            int[,] m = new int[n, n];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    m[i, j] = INF;
            for (int i = 0; i < n; i++)
                m[i, i] = 0;
            return m;
        }
    }
    class Time {
        public bool isLeapYear(int y) { return (y % 400 == 0 || (y % 4 == 0 && y % 100 != 0)); }
    }
    class BucketSort {
        public int[] bucket;
        public void Init(int[] a) {
            bucket = new int[a.Max() + 1];
            for (int i = 0; i < a.Length; ++i) ++bucket[a[i]];
            for (int i = 0, j = 0; j < bucket.Length; ++j)
                for (int k = bucket[j]; k != 0; --k, ++i) a[i] = j;

        }
    }
    #endregion
    #region Ex
    static class StringEX {//文字
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
        public static int toInt(this string s) { int n; return (int.TryParse(s.TrimStart('0'), out n)) ? n : 0; }
        public static int toInt(this char c) { return toInt(c.ToString()); }
        public static int toInt(this char[] c) { return toInt(new string(c)); }
    }
    static class NumericEx {//数値
        public static string pad0<T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
    }
    static class ArrayEX {
        public static T[] Sort<T>(this T[] a) { Array.Sort(a); return a; }
        public static void Set<T>(this T[] a, T v) {
            for (int i = 0; i < a.Length; i++) { a[i] = v; }
        }
        public static void Set<T>(this T[,] a, T v) {
            for (int i = 0; i < a.GetLength(0); i++)
                for (int j = 0; j < a.GetLength(1); j++)
                    a[i, j] = v;
        }
    }
    #endregion
}