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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
	static void solve() {
		int n = ni();
		int[] a = na(n);
		sort(a);
		long[] cum = new long[n+1];
		for(int i=0;i<n;i++)cum[i+1] = cum[i] + a[i];
		int cnt = 0;
		int[] mustBeOver = new int[n];
		
		for(int i=n-1;i>0;i--) {
			mustBeOver[i-1] = max(mustBeOver[i] - a[i], (a[i]+1)/2);
		}
		
		for(int i=n;i>0;i--) {
			if(cum[i] >= mustBeOver[i-1])cnt++;
		}
		out.println(cnt);
	}

	//constant
	static final long mod = (long) 1e9 + 7;
	static final int dx[] = { -1, 0, 1, 0 }, dy[] = { 0, -1, 0, 1 };
	static final int[] dx8 = { -1, -1, -1, 0, 0, 1, 1, 1 }, dy8 = { -1, 0, 1, -1, 1, -1, 0, 1 };
	static final int inf = Integer.MAX_VALUE / 2;
	static final long linf = Long.MAX_VALUE / 3;
	static final double dinf = Double.MAX_VALUE / 3;
	static final double eps = 1e-10;
	static final double pi = Math.PI;
	static StringBuilder sb = new StringBuilder();
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";

	//libraries
	static void reverse(int ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(long ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(double ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void reverse(char ar[]) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static String getReverse(String s) {
		char c[] = s.toCharArray();
		reverse(c);
		s = String.valueOf(c);
		return s;
	}

	static <T> void reverse(List<T> ls) {
		int sz = ls.size();
		for (int i = 0; i < sz / 2; i++) {
			T t = ls.get(i);
			ls.set(i, ls.get(sz - 1 - i));
			ls.set(sz - 1 - i, t);
		}
	}

	static <T> void reverse(T[] ar) {
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			T t = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = t;
		}
	}

	static void sbnl() {//StringBuilderに改行文字をappendする
		sb.append("\n");
	}

	static int lowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(int[] a, int x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(long[] a, long x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(double[] a, double x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int lowerBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] < x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int upperBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] <= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rlowerBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] > x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static int rupperBound(char[] a, char x) {
		int l = -1, r = a.length;
		while (r - l > 1) {
			int c = (l + r) / 2;
			if (a[c] >= x) {
				l = c;
			} else {
				r = c;
			}
		}
		return r;
	}

	static <T> int lowerBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) >= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) >= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int upperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) > 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) > 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int rupperBound(List<T> ls, T x) throws RuntimeException {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) < 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) < 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static <T> int rlowerBound(List<T> ls, T x) {
		if (ls.size() == 0)
			return -1;
		if (ls.get(0) instanceof Integer) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Long) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) <= 0 ? 1 : -1);
		} else if (ls.get(0) instanceof Double) {
			return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) <= 0 ? 1 : -1);
		} else {
			System.err.println(
					String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName()));
			throw new RuntimeException();
		}
	}

	static int[] concat(int x, int arr[]) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}

	static int[] concat(int arr[], int x) {
		int ret[] = new int[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}

	static long[] concat(long x, long arr[]) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 1, ret.length - 1);
		ret[0] = x;
		return ret;
	}

	static long[] concat(long arr[], long x) {
		long ret[] = new long[arr.length + 1];
		System.arraycopy(arr, 0, ret, 0, ret.length - 1);
		ret[ret.length - 1] = x;
		return ret;
	}

	static int max(int x, int y) {
		return Math.max(x, y);
	}

	static int min(int x, int y) {
		return Math.min(x, y);
	}

	static int max(int x, int y, int z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static int min(int x, int y, int z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static long max(long x, long y) {
		return Math.max(x, y);
	}

	static long min(long x, long y) {
		return Math.min(x, y);
	}

	static long max(long x, long y, long z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static long min(long x, long y, long z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static double max(double x, double y) {
		return Math.max(x, y);
	}

	static double min(double x, double y) {
		return Math.min(x, y);
	}

	static double max(double x, double y, double z) {
		x = Math.max(x, y);
		x = Math.max(x, z);
		return x;
	}

	static double min(double x, double y, double z) {
		x = Math.min(x, y);
		x = Math.min(x, z);
		return x;
	}

	static void sort(int[] ar) {
		Arrays.sort(ar);
	}

	static void sort(long[] ar) {
		Arrays.sort(ar);
	}

	static void sort(double[] ar) {
		Arrays.sort(ar);
	}

	static void sort(char[] ar) {
		Arrays.sort(ar);
	}

	static void rsort(int[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			int tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(long[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			long tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(double[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			double tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void rsort(char[] ar) {
		Arrays.sort(ar);
		int len = ar.length;
		for (int i = 0; i < len / 2; i++) {
			char tmp = ar[i];
			ar[i] = ar[len - 1 - i];
			ar[len - 1 - i] = tmp;
		}
	}

	static void fill(int arr[], int x) {
		Arrays.fill(arr, x);
	}

	static void fill(long arr[], long x) {
		Arrays.fill(arr, x);
	}

	static void fill(boolean arr[], boolean x) {
		Arrays.fill(arr, x);
	}

	static void fill(double arr[], double x) {
		Arrays.fill(arr, x);
	}

	static void fill(int arr[][], int x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(long arr[][], long x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(double arr[][], double x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	static void fill(boolean arr[][], boolean x) {
		for (int i = 0; i < arr.length; i++)
			Arrays.fill(arr[i], x);
	}

	//MOD culc
	static long plus(long x, long y) {
		long res = (x + y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long sub(long x, long y) {
		long res = (x - y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long mul(long x, long y) {
		long res = (x * y) % mod;
		return res < 0 ? res + mod : res;
	}

	static long div(long x, long y) {
		long res = x * pow(y, mod - 2) % mod;
		return res < 0 ? res + mod : res;
	}

	static long pow(long x, long y) {
		if (y < 0)
			return 0;
		if (y == 0)
			return 1;
		if (y % 2 == 1)
			return (x * pow(x, y - 1)) % mod;
		long root = pow(x, y / 2);
		return root * root % mod;
	}

	public static void main(String[] args) throws Exception {
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	//input
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;

	private static int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	@SuppressWarnings("unused")
	private static double nd() {
		return Double.parseDouble(ns());
	}

	@SuppressWarnings("unused")
	private static char nc() {
		return (char) skip();
	}

	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	@SuppressWarnings("unused")
	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	@SuppressWarnings("unused")
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	@SuppressWarnings("unused")
	private static long[] nla(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}

	private static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	@SuppressWarnings("unused")
	private static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

}