Problem:
Score : 700 points

Problem Statement

Snuke loves constructing integer sequences.

There are N piles of stones, numbered 1 through N.
The pile numbered i consists of a_i stones.

Snuke will construct an integer sequence s of length Σa_i, as follows:

Among the piles with the largest number of stones remaining, let x be the index of the pile with the smallest index. Append x to the end of s.

Select a pile with one or more stones remaining, and remove a stone from that pile.

If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.

We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers 1,2,3,...,N, how many times does it occur in the lexicographically smallest sequence?

Constraints

1 ≤ N ≤ 10^{5}

1 ≤ a_i ≤ 10^{9}

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{N}

Output

Print N lines. The i-th line should contain the number of the occurrences of the integer i in the lexicographically smallest sequence that can be constructed.

Sample Input 1

2
1 2

Sample Output 1

2
1

The lexicographically smallest sequence is constructed as follows:

Since the pile with the largest number of stones remaining is pile 2, append 2 to the end of s. Then, remove a stone from pile 2.

Since the piles with the largest number of stones remaining are pile 1 and 2, append 1 to the end of s (we take the smallest index). Then, remove a stone from pile 2.

Since the pile with the largest number of stones remaining is pile 1, append 1 to the end of s. Then, remove a stone from pile 1.

The resulting sequence is (2,1,1). In this sequence, 1 occurs twice, and 2 occurs once.

Sample Input 2

10
1 2 1 3 2 4 2 5 8 1

Sample Output 2

10
7
0
4
0
3
0
2
3
0

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//void __(){
//    _(int,n);
//    _(vi,a,n);
//    vpii b;
//    rep(i,n)
//        b.pb({a[i],i});
//    b.pb({0,-1});
//    sort(rall(b));
//    int smallest_index = n-1;
//    int last_h = b[0].X;
//    vi ans(n);
//    rep(i,n+1){
//        ans[smallest_index] += (last_h-b[i].X)*i;
//        last_h = b[i].X;
//        smallest_index = min(smallest_index,b[i].Y);
//    }
//    print_vn ans;
//}
//
#include <iomanip>
#include <algorithm>
#include <cassert>
#include <vector>
#include <utility>
#include <iostream>
#include <string>
#define pb push_back
#define REP_ZERO_INT(i,r) for(int i = 0; i < r; ++i)
#define GET_REP_MACRO(_1,_2,_3,_4,NAME,...) NAME
#define rep(...) GET_REP_MACRO(__VA_ARGS__,REP_ANY,REP_INT,REP_ZERO_INT)(__VA_ARGS__)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define sz(v) ll(v.size())
#define X first
#define Y second
#define T1 template<typename T> static
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pii;
typedef vector<pii> vpii;
T1 ostream& operator<<(ostream& stream, const vector<T>& t);
T1 istream& read(T, T, istream& = cin);
T1 istream& operator>>(istream& stream, vector<T>& t){
    return read(all(t), stream);
}
T1 istream& read(T b, T e, istream& stream){
    for(T it = b; it != e; ++it)
        stream >> *it;
    return stream;
}
struct _print {
    string sep,end;
    bool space;
    ostream &stream;
    _print(string _sep=" ",string _end="\n",
            ostream &_stream = cout)
        : sep(_sep),end(_end),space(false),
            stream(_stream) {}
    ~_print() { stream << end; }
    template <typename T>
        _print &operator , (const T &t) {
            if (space) stream << sep;
            space = true;
            stream << t;
            return *this;
        }
};
struct _print2{
    string s1,s2,end;
    bool space;
    ostream &stream;
    _print2(string _s1 = " ", string _s2 = " ", string _end="\n", ostream &_stream = cout)
        :s1(_s1),s2(_s2),end(_end),space(false),
        stream(_stream) {}
    ~_print2() { stream << end; }
    template <typename T>
        _print2 &operator , (const T &t) {
            for(auto _ : t){
                if (space) stream << s1;
                space = true;
                _print p(s2,"",stream);
                    p,_;
            }
            return *this;
        }
};
#define print_vn _print2("\n"," ","\n"),
#define INPUT_WITHOUT_INIT(type,name) type name; cin >> name
#define _IWI(type,name,...) type name(__VA_ARGS__); cin >> name
#define GET_INPUT_MACRO(_1,_2,_3,_4,_5,_6,_7,_8,NAME,...) NAME
#define _(...) GET_INPUT_MACRO(__VA_ARGS__,_IWI,_IWI,_IWI,_IWI,_IWI,_IWI,INPUT_WITHOUT_INIT)(__VA_ARGS__)
void __(){
    _(int,n);
    _(vi,a,n);
    vpii b;
    rep(i,n)
        b.pb({a[i],i});
    b.pb({0,-1});
    sort(rall(b));
    int smallest_index = n-1;
    int last_h = b[0].X;
    vi ans(n);
    rep(i,n+1){
        ans[smallest_index] += (last_h-b[i].X)*i;
        last_h = b[i].X;
        smallest_index = min(smallest_index,b[i].Y);
    }
    print_vn ans;
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);
        __();
}