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 Ruby (2.3.3) (judge verdict: Accepted)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
    return Array.new(size1){init}
  else
    return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

class UnionFindTree
    attr_accessor:par,:rank
    def initialize(n)
        @par=Array.new(n){|i| i}
        @rank=array(n,0)
    end

    def find(x)
        return x if @par[x]==x
        @par[x]=find(@par[x])
        return @par[x]
    end

    def union(x,y)
        x=find(x)
        y=find(y)
        return if x==y
        if @rank[x]<@rank[y]
            @par[x]=y
        else
            @par[y]=x
            @rank[x]+=1 if @rank[x]==@rank[y]
        end
    end

    def same?(x,y)
        return find(x)==find(y)
    end
end
N=gets.to_i
a=get_i.sort
ans=0
uft=UnionFindTree.new(N)
(N-1).times do|i|
  uft.union(i,i+1) if a[i+1]<=2*a[i]
  a[i+1]+=a[i]
end
ans=0
N.times do|i|
  ans+=1 if uft.same?(i,N-1)
end
puts ans