Problem:
Counting Sort

Counting sort can be used for sorting elements in an array which each of the n input elements is an integer in the range 0 to k. The idea of counting sort is to determine, for each input element x, the number of elements less than x as C[x]. This information can be used to place element x directly into its position in the output array B. This scheme must be modified to handle the situation in which several elements have the same value. Please see the following pseudocode for the detail:

Counting-Sort(A, B, k)
1 for i = 0 to k
2 do C[i] = 0
3 for j = 1 to length[A]
4 do C[A[j]] = C[A[j]]+1
5 /* C[i] now contains the number of elements equal to i */
6 for i = 1 to k
7 do C[i] = C[i] + C[i-1]
8 /* C[i] now contains the number of elements less than or equal to i */
9 for j = length[A] downto 1
10 do B[C[A[j]]] = A[j]
11 C[A[j]] = C[A[j]]-1

Write a program which sorts elements of given array ascending order based on the counting sort.

Input

The first line of the input includes an integer n, the number of elements in the sequence.

In the second line, n elements of the sequence are given separated by spaces characters.

Output

Print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character.

Constraints

1 ≤ n ≤ 2,000,000

0 ≤ A[i] ≤ 10,000

Sample Input 1

7
2 5 1 3 2 3 0

Sample Output 1

0 1 2 2 3 3 5

Solution in JAVA (judge verdict: Memory Limit Exceeded)

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


public class Main {
	static int n = 0;
	
	public static void counting_sort(int[] a) {
		// b is the sorted array
		int[] b = new int[n];
		
		// c is the counting array
		int[] c = new int[2000000+1];
		Arrays.fill(c, 0);
		
		// counting occurrences of each a[i]
		for (int i = 0; i < n; i++) {
			c[a[i]]++;
		} 
		
		// count the number less than or equal to a[i]
		for (int i = 1; i <= 2000000; i++) {
			c[i] = c[i] + c[i-1];
		}
	
		
		// with each a[i], place it in the right position
		for (int i = n-1; i >= 0; i--) {
			
			// a[i] will be placed in the index that right after the number of elements <= a[i]
			b[c[a[i]]-1] = a[i];
			// ...
			c[a[i]]--;
		}
		
		for (int i = 0; i < n-1; i++) System.out.print(b[i] + " ");
		System.out.println(b[n-1]);
	}
	
	public static void main (String args[]) {
		@SuppressWarnings("resource")
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) 
			a[i] = sc.nextInt();
		counting_sort(a);
	}
}