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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

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

public class Main {
    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);
        int t = 1;
        Solver s = new Solver();
        for (int i = 1; i <= t; i++) {
            s.solve(i, in, out);
        }
        out.close();
    }

}

class Solver {

    private static final int INF = (int) 1e9;

    static class Pair {
        int val, idx;
    }

    void solve(int test, InputReader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        Pair[] a = new Pair[n + 1];
        a[0] = new Pair();
        a[0].val = 0;
        a[0].idx = INF;
        for (int i = 1; i <= n; i++) {
            a[i] = new Pair();
            a[i].val = in.nextInt();
            a[i].idx = i;
        }
        Arrays.sort(a, 1, n + 1, new Comparator<Pair>() {
            @Override
            public int compare(Pair o1, Pair o2) {
                if (o1.val != o2.val) return Integer.compare(o1.val, o2.val);
                return Integer.compare(o1.idx, o2.idx);
            }
        });
//        for (int i = 1; i <= n; i++) out.print(a[i].val + " ");
//        out.println();
//        for (int i = 1; i <= n; i++) out.print(a[i].idx + " ");
//        out.println();
        TreeMap<Integer, Long> map = new TreeMap<>();
        int it = n, size = 1, minIndex = Integer.MAX_VALUE;
        while (it >= 1) {
            if (a[it].val > a[it - 1].val) {
                minIndex = Math.min(minIndex, a[it].idx);
                map.put(minIndex, map.get(minIndex) == null ?  size * (long) (a[it].val - a[it - 1].val) : map.get(minIndex) + size * (long) (a[it].val - a[it - 1].val));
            }
//            out.println("Min Index " + minIndex);
            it--;
            size++;
        }
        for (int i = 1; i <= n; i++) {
            if (map.containsKey(i)) {
                out.println(map.get(i));
            } else {
                out.println(0);
            }
        }
    }
}

class InputReader {
    BufferedReader br;
    StringTokenizer st;

    public InputReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
        st = null;
    }

    public String next() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return st.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}