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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

// -*- coding: utf-8 -*-
//import java.awt.*;
import java.io.*;
import java.math.*;
import java.text.*;
import java.util.*;

public class Main {
  public static void main(String[] args) {
    InputStream inputStream;
    if (args.length > 0 && args[0].equals("devTesting")) {
      try {
        inputStream = new FileInputStream(args[1]);
      } catch(FileNotFoundException e) {
        throw new RuntimeException(e);
      }
    } else {
      inputStream = System.in;
    }
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    TaskB solver = new TaskB();
    solver.solve(1, in, out);
    out.close();
  }
  
  static class TaskB {    
    int n;
    int[] a;
    
    void solve(int testNumber, InputReader in, PrintWriter out) {
      n = in.nextInt();
      a = new int[n];
      for (int i= 0; i < n; ++i) {
        a[i] = in.nextInt();
      }
      Arrays.sort(a);
      long cnt = 0, acc = a[0];
      for (int i = 1; i < n; ++i) {
        if (2 * acc >= a[i]) {
          ++cnt;
        } else {
          cnt = 0;
        }
        acc += a[i];
      }
      ++cnt;
      System.err.println(cnt);
    }
    
    int i(long x) {
      return (int) x;
    }
    
    <T> void heapsort(T[] a, int s, int e) {
      Queue<T> queue = new PriorityQueue<>();
      for (int i = s; i <= e; ++i)
        queue.add(a[i]);
      for (int i = s; i <= e; ++i)
        a[i] = queue.poll();
    }    
    
  }
      
  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream));
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }
    
    public String nextLine() {
      try {
        return reader.readLine();
      } catch(IOException e) {
        throw new RuntimeException(e);
      }
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

    public long nextLong() {
      return Long.parseLong(next());
    }
    
    public double nextDouble() {
      return Double.parseDouble(next());
    }

    public boolean hasInput() {
      try {
        if (tokenizer != null && tokenizer.hasMoreTokens()) {
          return true;
        }
        reader.mark(1);
        int ch = reader.read();
        if (ch != -1) {
          reader.reset();
          return true;
        }
        return false;
      } catch(IOException e) {
        throw new RuntimeException(e);
      }
    }
    
  }
}