Problem:
Score : 400 points

Problem Statement

Snuke found N strange creatures.
Each creature has a fixed color and size. The color and size of the i-th creature are represented by i and A_i, respectively.

Every creature can absorb another creature whose size is at most twice the size of itself.
When a creature of size A and color B absorbs another creature of size C and color D (C \leq 2 \times A), they will merge into one creature of size A+C and color B.
Here, depending on the sizes of two creatures, it is possible that both of them can absorb the other.

Snuke has been watching these creatures merge over and over and ultimately become one creature.
Find the number of the possible colors of this creature.

Constraints

2 \leq N \leq 100000

1 \leq A_i \leq 10^9

A_i is an integer.

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 colors of the last remaining creature after the N creatures repeatedly merge and ultimately become one creature.

Sample Input 1

3
3 1 4

Sample Output 1

2

The possible colors of the last remaining creature are colors 1 and 3.
For example, when the creature of color 3 absorbs the creature of color 2, then the creature of color 1 absorbs the creature of color 3, the color of the last remaining creature will be color 1.

Sample Input 2

5
1 1 1 1 1

Sample Output 2

5

There may be multiple creatures of the same size.

Sample Input 3

6
40 1 30 2 7 20

Sample Output 3

4

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace AGC011B
{
    class Program
    {
        public static void Solve(Input input)
        {
            var n = input.NextInt();
            var a = input.NextInt(n);

            // 最後まで残れる生き物が何体いるか
            Array.Sort(a);

            var sums = new long[n];
            sums[0] = a[0];
            for (int i = 1; i < n; i++)
            {
                sums[i] = sums[i - 1] + a[i];
            }

            // 大きい方から考えていく
            var viableCount = 1;
            for (int i = n - 1 - 1; i >= 0; i--)
            {
                // 自分以下の生き物を全て吸収して、一つ上の生き物を吸収できなければ、最後まで生き残れない
                if (sums[i] * 2 < a[i + 1]) break;

                viableCount++;
            }

            Console.WriteLine(viableCount);
        }

        #region Main
        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // そのときにTLEするのはアルゴリズムが悪いせいだし、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();

            // 仮想的に標準入力をセットする
            // テスト入力したまま提出することがままあるので……
#if DEBUG
            input.SetText("");
#endif

            Solve(input);

            Console.Out.Flush();
        }
        #endregion

        #region Competitive Template
#pragma warning disable CS0414
        static readonly int MOD = (int)1e9 + 7;
        static readonly int[] dx = { 1, 0, -1, 0 };
        static readonly int[] dy = { 0, 1, 0, -1 };
        /// <summary> 左上が原点 </summary>
        static readonly char[] dir = { 'R', 'U', 'L', 'D' };
#pragma warning restore CS0414

        public class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            readonly StreamReader sr;
            readonly Queue<string> queue;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            public Input(string path = "")
            {
                queue = new Queue<string>();

                if (string.IsNullOrEmpty(path)) { sr = new StreamReader(Console.OpenStandardInput()); }
                else { sr = new StreamReader(path); }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                    SetText(item);
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            public bool SetText(string s)
            {
                if (string.IsNullOrEmpty(s)) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                    queue.Enqueue(elem);

                return true;
            }

            /// <summary>
            /// 要素が存在するか
            /// </summary>
            public bool Any() => queue.Any() || Read();

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            bool Read()
            {
                if (!SetText(sr.ReadLine())) return false;

                if (!queue.Any()) return Read();

                return queue.Any();
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            public string Next()
            {
                if (!queue.Any() && !Read()) return "";

                return queue.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            bool Accumulate(int n)
            {
                while (queue.Count() < n)
                    if (!Read()) return false;

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!Accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(queue.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            public static T[][] Create2DArray<T>(int d1, int d2, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v)
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                    Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}