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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
/**
 * 境界部分には気をつける(そこだけ別で処理するというのもあり)
 * 逆再生することで簡単になることもある
 */
public class Main {
	public int cnt = 0;
	public static final BigDecimal TWO = new BigDecimal(2);
	public static final BigDecimal THREE = new BigDecimal(3);

    public Main() {
    }

    public static void main(String[] args ) {
            Main main = new Main();
            main.exec();
    }

    public void exec() {
        BufferedReader bf = null;
        try{
            bf = new BufferedReader(new InputStreamReader(System.in));
            exec_body(bf);
        } catch (IOException e) {
            e.printStackTrace();
        }
        finally{
            if( bf != null ) {
                try {
                    bf.close();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }
    }

    public void exec_body( BufferedReader bf ) throws IOException {
    		bf.readLine();
    		String line = bf.readLine();
    		int[] vals = toIList(line);

    		// 配列の初期化
    		int maxVal = max(vals);
    		int minVal = min(vals);
    		int[] counts = new int[maxVal-minVal+1];
    		for( int ii = 0; ii < counts.length; ii++ ) {
    			counts[ii] = 0;
    		}

    		// 計数
    		for( int ii = 0; ii < vals.length; ii++ ) {
    			int val = vals[ii];
    			counts[val-minVal]++;
    		}

    		// 足す
    		for( int ii = 1; ii < counts.length; ii++ ) {
    			counts[ii] = counts[ii] + counts[ii-1];
    		}

    		// sort処理を行う
    		int[] ans = new int[vals.length];
    		for( int ii = vals.length -1; ii >= 0; ii-- ) {
    			int val = vals[ii];
    			int index = counts[val-minVal];
    			ans[index-1] = val;
    			counts[val-minVal]--;
    		}

    		print(ans);
    }

    public int max( int[] ary ) {
    		int ret = Integer.MIN_VALUE;
    		for( int ii = 0; ii < ary.length; ii++ ) {
    			if( ret < ary[ii] ) {
    				ret = ary[ii];
    			}
    		}

    		return ret;
    }

    public int min( int[] ary ) {
		int ret = Integer.MAX_VALUE;
		for( int ii = 0; ii < ary.length; ii++ ) {
			if( ret > ary[ii] ) {
				ret = ary[ii];
			}
		}

		return ret;
    }

    public static int[] toIList( String str ) {
        String[] elements = str.split(" ");
        int[] ret = new int [elements.length];
        for( int i = 0; i < elements.length; i++ ) {
            ret[i] = Integer.valueOf(elements[i]);
        }

        return ret;
    }

    public static void print( int[] ary ) {
    		if( ary == null || ary.length == 0 ) {
    			return;
    		}

    		StringBuilder bd = new StringBuilder();
    		for( int i = 0; i < ary.length; i++ ) {
    			if( i != 0 ) {
    				bd.append(" ");
    			}
    			bd.append(ary[i]);
    		}

    		System.out.println(bd.toString());
    }
}