Problem:
Score : 1000 points

Problem Statement

There are N integers written on a blackboard. The i-th integer is A_i, and the greatest common divisor of these integers is 1.

Takahashi and Aoki will play a game using these integers. In this game, starting from Takahashi the two player alternately perform the following operation:

Select one integer on the blackboard that is not less than 2, and subtract 1 from the integer.

Then, divide all the integers on the black board by g, where g is the greatest common divisor of the integers written on the blackboard.

The player who is left with only 1s on the blackboard and thus cannot perform the operation, loses the game.
Assuming that both players play optimally, determine the winner of the game.

Constraints

1 ≦ N ≦ 10^5

1 ≦ A_i ≦ 10^9

The greatest common divisor of the integers from A_1 through A_N is 1.

Input

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

N
A_1 A_2 … A_N

Output

If Takahashi will win, print First. If Aoki will win, print Second.

Sample Input 1

3
3 6 7

Sample Output 1

First

Takahashi, the first player, can win as follows:

Takahashi subtracts 1 from 7. Then, the integers become: (1,2,2).

Aoki subtracts 1 from 2. Then, the integers become: (1,1,2).

Takahashi subtracts 1 from 2. Then, the integers become: (1,1,1).

Sample Input 2

4
1 2 4 8

Sample Output 2

First

Sample Input 3

5
7 8 8 8 8

Sample Output 3

Second

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using StringBuilder = System.Text.StringBuilder;
using System.Numerics;
using Point = System.Numerics.Complex;
using Number = System.Int64;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var n = sc.Integer();
            var a = sc.Long(n);
            var sum = 0L;
            foreach (var x in a)
                sum += x - 1;
            var seg = new RMQSegmentTree(n);
            for (int i = 0; i < n; i++)
                seg.Update(i, a[i]);
            var otaku = a.Sum();
            var all = 0;
            for (int i = 0; i < n; i++)
            {
                if (a[i] == 1) continue;
                var l = seg.Query(0, i);
                var r = seg.Query(i + 1, n);
                var x = a[i] - 1;
                x = MathEx.GCD(x, l);
                x = MathEx.GCD(x, r);
                if (x != 1)
                {
                    var y = (otaku - 1) / x;
                    if ((y - n) % 2 != 0)
                    {
                        IO.Printer.Out.WriteLine("First");
                        throw new Exception();
                        return;
                    }
                    else all++;
                }
            }

            if (sum % 2 == 0 || all == n) IO.Printer.Out.WriteLine("Second");
            else IO.Printer.Out.WriteLine("First");



        }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex
{
    static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
    static public void Main()
    {
        var solver = new Program.Solver();
        solver.Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer: StreamWriter
    {
        static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
        public static Printer Out { get; set; }
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
        public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
        public void Write<T>(string format, T[] source) { base.Write(format, source.OfType<object>().ToArray()); }
        public void WriteLine<T>(string format, T[] source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
        public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n) { return enumerate(n, Char); }
        public string[] Scan(int n) { return enumerate(n, Scan); }
        public double[] Double(int n) { return enumerate(n, Double); }
        public int[] Integer(int n) { return enumerate(n, Integer); }
        public long[] Long(int n) { return enumerate(n, Long); }
    }
}
#endregion
#region HashMap<K,V>
public class HashMap<K, V>: Dictionary<K, V>
//where V : new()
{
    public HashMap() : base() { }
    public HashMap(int cap) : base(cap) { }
    new public V this[K i]
    {
        get
        {
            V v;
            return TryGetValue(i, out v) ? v :
                base[i] = default(V);
            //base[i] = new V();
        }
        set { base[i] = value; }
    }
}
#endregion

#region RMQ Segment Tree
public class RMQSegmentTree
{
    const Number ZERO = Number.MaxValue;
    int n;
    Number[] data;
    public RMQSegmentTree(int size)
    {
        n = 1;
        while (n < size)
            n <<= 1;
        data = new Number[n << 1];
    }
    public void Update(int k, Number v)
    {
        k += n;
        data[k] = v;
        k >>= 1;
        while (k > 0)
        {
            data[k] = merge(data[k << 1], data[(k << 1) + 1]);
            k >>= 1;
        }

    }
    public Number Query(int a, int b) { return query(a, b, 1, 0, n); }
    private Number query(int a, int b, int k, int l, int r)
    {
        if (r <= a || b <= l)
            return 0;
        if (a <= l && r <= b)
            return data[k];
        else
        {
            var vl = query(a, b, k << 1, l, (l + r) >> 1);
            var vr = query(a, b, (k << 1) + 1, (l + r) >> 1, r);
            return merge(vl, vr);
        }
    }
    Number merge(Number l, Number r)
    {
        return MathEx.GCD(l, r);
    }
    public Number[] Items
    {
        get
        {
            var ret = new Number[n];
            for (int i = 0; i < n; i++)
                ret[i] = data[i + n];
            return ret;
        }
    }

}
#endregion

#region gcd,lcm
static public partial class MathEx
{

    static public Number GCD(Number n, Number m)
    {
        bool f = true;
        for (; n != 0 && m != 0; f ^= true)
        {
            if (f) m %= n;
            else n %= m;
        }
        return n == 0 ? m : n;
    }
    static public Number LCM(Number n, Number m)
    {
        return (n / GCD(n, m)) * m;
    }
    static public Number GCD(params Number[] a)
    {
        var gcd = a[0];
        foreach (var x in a)
            gcd = GCD(gcd, x);
        return gcd;
    }

}
#endregion