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 C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

namespace ext {
	template <class T>
	struct vec_type;
	template <class T>
	constexpr bool is_vec_v;
	using namespace std;
	template<class T>
	struct Vector : std::vector<T> {
		using std::vector<T>::vector;
		char dil = ' ';
		Vector<T> accum() {
			Vector<T> res(this->size() + 1);
			for (size_t i = 0; i < this->size(); i++) {
				res[i+1] = (*this)[i] + res[i];
			}
			return res;
		}
		template<class U = T>
		typename enable_if<is_vec_v<U>, Vector<T>>::type accum2D() {
			const size_t H = this->size();
			const size_t W = (*this)[0].size();
			using S = typename vec_type<U>::type;
			Vector<T> res(H + 1, Vector<S>(W + 1));
			for (size_t i = 0; i < H; i++) {
				for (size_t j = 0; j < W; j++) {
					res[i+1][j+1] = (*this)[i][j];
					res[i+1][j+1] += res[i][j+1];
					res[i+1][j+1] += res[i+1][j];
					res[i+1][j+1] -= res[i][j];
				}
			}
			return res;
		}
		Vector<T> zaatsu() {
			map<T, int> m;
			for (auto& e: *this) m[e] = 1;
			int count = 0;
			for (auto& e: m) e.second = count++;
			Vector<T> res = *this;
			for (auto& e: res) e = m[e];
			return res;
		}
		friend istream& operator>>(istream& is, Vector<T>& t) {
			for (auto& e: t) cin >> e;
			return is;
		}
		friend ostream& operator<<(ostream& os, Vector<T>& t) {
			t.print(' ', os);
			return os;
		}
		void print(char del = ' ', ostream& os = cout) {
			for (size_t i = 0; i < this->size(); i++) {
				os << (*this)[i];
				if (i + 1 != this->size()) os << del;
				os.flush();
			}
		}
		void println(char del = ' ', ostream& os = cout) {
			print(del, os);
			cout << endl;
		}
		long long crossing_merge() {
			auto t = *this;
			return t.crossing_merge_sub();
		}
		// [min_v, max_v)
		long long crossing_bit(T min_v = -1, T max_v = -1) {
			if (min_v == -1) min_v = this->min();
			if (max_v == -1) max_v = this->max() + 1;
			Vector<T> bit(max_v - min_v + 1, 0);
			long long res = 0;
			for (auto e: *this) {
				e = max_v - e;
				for (size_t x = e - 1; x; x -= x & -x) {
					res += bit[x];
				}
				for (size_t x = e; x < bit.size() ; x += x & -x) {
					bit[x]++;
				}
			}
			return res;
		}
		bool permutation() {
			return next_permutation(this->begin(), this->end());
		}
		T& max() {
			return *max_element(this->begin(), this->end());
		}
		T& min() {
			return *min_element(this->begin(), this->end());
		}
private:
		long long crossing_merge_sub() {
			if (this->size() == 1) return 0;
			int x = this->size() / 2;
			Vector<T> left(this->begin(), this->begin() + x);
			Vector<T> right(this->begin() + x, this->end());
			long long res = left.crossing_merge_sub() + right.crossing_merge_sub();
			left.push_back(numeric_limits<T>::max()); right.push_back(numeric_limits<T>::max());
			size_t l = 0, r = 0;
			while (l + r < this->size()) {
				if (left[l] < right[r]) {
					(*this)[l+r] = left[l];
					l++;
				} else {
					(*this)[l+r] = right[r];
					r++;
					res += x - l;
				}
			}
			return res;
		}
	};
	template <class T>
	struct vec_type : std::false_type {};
	template <class T>
	struct vec_type<Vector<T>> : std::true_type {
		using type = T;
	};
	template <class T>
	constexpr bool is_vec_v = vec_type<T>::value;
}
using namespace ext;

int main() {
	int n; cin >> n;
	Vector<int> v(n); cin >> v;
	vector<int> c(v.max() + 1);
	for (auto& x : v) {
		c[x]++;
	}
	bool f = false;
	int m = 0;
	for (auto& x : c) {
		while (x--) {
			if (f) cout << " ";
			f = true;
			cout << m;
		}
		m++;
	}
	cout << endl;
}