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.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {

    static int N;
    static Pile[] P;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();

        P = new Pile[N];
        for (int i = 0; i < N; i++) {
            int size = sc.nextInt();
            P[i] = new Pile(i+1, size);
        }

        PrintWriter pw = new PrintWriter(System.out);
        for (long l : solve()) {
            pw.println(l);
        }
        pw.flush();
    }

    static long[] solve() {
        PriorityQueue<Pile> q = new PriorityQueue<>((p1, p2) -> {
            if( p1.size != p2.size ) {
                return Integer.compare(p2.size, p1.size); // sizeで降順
            } else {
                return Integer.compare(p1.no, p2.no);
            }
        });
        q.addAll( Arrays.asList(P) );

        long[] cnt = new long[N];

        Pile first = q.poll();
        int no = first.no;
        int size = first.size;
        int piles = 1;
        while( !q.isEmpty() ) {
            Pile p = q.peek();
            if( p.size == size ) {
                piles++;
                q.poll();

            } else {
                int diff = size - p.size;
                cnt[no-1] += (long)diff * piles;
                if( p.no < no ) {
                    no = p.no;
                }
                size -= diff;
                piles++;
                q.poll();
            }
        }
        cnt[no-1] += (long)size * piles;
        return cnt;
    }

    static class Pile {
        int no, size;

        public Pile(int no, int size) {
            this.no = no;
            this.size = size;
        }
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }
}