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
//------------------------------------------
#include <bits/stdc++.h>

using namespace std;

// conversion
//------------------------------------------
inline int toInt(string s) {
    int v;
    istringstream sin(s);
    sin >> v;
    return v;
}
template <class T>
inline string toString(T x) {
    ostringstream sout;
    sout << x;
    return sout.str();
}

// math
//-------------------------------------------
template <class T>
inline T sqr(T x) {
    return x * x;
}

// typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

// container util
//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i, c) \
    for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define SORT(c) sort((c).begin(), (c).end())

// repetition
//------------------------------------------
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define FORD(i, a, b) for (int i = (a); i > (b); --i)
#define REP(i, n) FOR(i, 0, n)
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)

// constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int INF_INT = 2147483647;
const LL INF_LL = 9223372036854775807;

// clear memory
//--------------------------------------------
#define CLR(a) memset((a), 0, sizeof(a))

// vector
//--------------------------------------------
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
    for (T &x : vec) is >> x;
    return is;
}

// pair
//--------------------------------------------
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) {
    os << "(" << pair_var.first << ", " << pair_var.second << ")";
    return os;
}

// vector
//--------------------------------------------
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}

// list
//--------------------------------------------
template <typename T>
ostream &operator<<(ostream &os, const list<T> &lst) {
    os << "{";
    REPI(itr, lst) {
        os << *itr;
        itr++;
        if (itr != lst.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}

// map
//--------------------------------------------
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
    os << "{";
    REPI(itr, map_var) {
        os << *itr;
        itr++;
        if (itr != map_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}

// set
//--------------------------------------------
template <typename T>
ostream &operator<<(ostream &os, set<T> &set_var) {
    os << "{";
    REPI(itr, set_var) {
        os << *itr;
        itr++;
        if (itr != set_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}

// dump
//--------------------------------------------
#define DUMPOUT cerr

void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail) {
    DUMPOUT << head;
    if (sizeof...(Tail) > 0) {
        DUMPOUT << ", ";
    }
    dump_func(std::move(tail)...);
}
#ifdef DEBUG_
#define DEB
#define dump(...)                                                       \
    DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                     \
            << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" \
            << endl                                                     \
            << "    ",                                                  \
        dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

int n;
int a[2000001], b[2000001];

void countingSort(int a[], int b[], int k) {
    int c[10001];
    REP(i, k + 1) c[i] = 0;
    REP(j, n) c[a[j + 1]]++;
    FOR(i, 1, k + 1) c[i] = c[i] + c[i - 1];
    REP(i, k + 1) dump(c[i]);
    FOR(j, 1, n + 1) {
        b[c[a[j]]] = a[j];
        c[a[j]]--;
    }
}

int main(void) {
    cin >> n;
    int k = 0;
    REP(i, n) {
        cin >> a[i + 1];
        k = max(k, a[i + 1]);
    };
    countingSort(a, b, k);
    FOR(i, 1, n + 1) {
        if (i != 1) cout << " ";
        cout << b[i];
    }
    cout << endl;
    return 0;
}