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++14 (GCC 5.4.1) (judge verdict: Accepted)

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>

using namespace std;

#define mp make_pair
#define pb push_back
#define sz(s) ((int) ((s).size()))

#ifdef DEBUG
#define eprintf(...) fprintf(stderr, __VA_ARGS__), fflush(stderr)
#else
#define eprintf(...) ;
#endif

typedef long long ll;
typedef long double ld;

const int inf = (int) 1.01e9;
const ld eps = 1e-11;
const ld pi = acos(-1.0L);

mt19937 mrand(random_device{} ());
int rnd(int x) {
  return mrand() % x;
}

const int mod = (int) 1e9 + 7;

void add(int & x, int y) {
  if ((x += y) >= mod) {
    x -= mod;
  }
}

int sum(int x, int y) {
  add(x, y);
  return x;
}

int mult(int x, int y) {
  return (ll) x * y % mod;
}

int power(int x, ll p) {
  int res = 1;
  while (p) {
    if (p & 1) {
      res = mult(res, x);
    }
    x = mult(x, x);
    p >>= 1;
  }
  return res;
}

int inv(int x) {
  return power(x, mod - 2);
}

void precalc() {
}

const int maxn = 1e5 + 100;

int n;
int a[maxn];

bool read() {
  if (scanf("%d", &n) < 1) {
    return false;
  }
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
  }
  return true;
}

void solve() {
  sort(a, a + n);
  ll sum = 0;
  int res = n;
  for (int i = 0; i < n; i++) {
    ll wass = sum;
    sum += a[i];
    if (sum > wass * 3) {
      res = min(res, n - i);
    }
  }
  printf("%d\n", res);
}

int main() {
  precalc();
#ifdef DEBUG
  assert(freopen("text.in", "r", stdin));
  assert(freopen("text.out", "w", stdout));
#endif

  while (read()) {
    solve();
#ifdef DEBUG
    eprintf("Time: %.3f\n", (double) clock() / CLOCKS_PER_SEC);
#endif
  }
  return 0;
}