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: Wrong Answer)

import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            solve(in);
        }
    }

    private static void solve(Scanner in) {
        int N = in.nextInt();
        Yama[] Y = new Yama[N];
        for (int i = 0; i < N; i++) {
            int a = in.nextInt();
            Y[i] = new Yama(a, i);
        }
        Arrays.sort(Y);

        long[] freq = new long[N];
        for (int j = 0; j < N;) {
            int aa = Y[j].a;
            int ii = Y[j].i;
            int cnt = 0;
            int k = j;
            while (k < N && aa == Y[k].a) {
                ii = Y[k].i;
                Y[k++].a--;
                cnt++;
            }
            freq[ii] += cnt;
            if (k < N && Y[j].a >= Y[k].a) {
                continue;
            }
            j = k + 1;
        }

        StringBuilder ans = new StringBuilder();
        for (long f : freq) {
            ans.append(f).append('\n');
        }
        System.out.println(ans);
    }
}

class Yama implements Comparable<Yama> {
    int a, i;

    Yama(int a, int i) {
        this.a = a;
        this.i = i;
    }

    @Override
    public int compareTo(Yama o) {
        if (o.a != a) {
            return o.a - a;
        }
        return o.i - i;
    }

    @Override
    public String toString() {
        return String.format("(a=%d,i=%d)", a, i);
    }
}

class Scanner implements Closeable {
    private final InputStream stream;
    private final byte[] buf = new byte[1024];
    private int cur;
    private int num;

    Scanner(InputStream stream) {
        this.stream = stream;
    }

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

    int nextInt() {
        return (int) nextLong();
    }

    long nextLong() {
        int c = read();
        while (isdel(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long l = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            l *= 10;
            l += c - '0';
            c = read();
        } while (!isdel(c));
        return l * sgn;
    }

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

    String next() {
        int c = read();
        while (isdel(c))
            c = read();
        StringBuilder s = new StringBuilder();
        do {
            s.appendCodePoint(c);
            c = read();
        } while (!isdel(c));
        return s.toString();
    }

    private int read() {
        if (num == -1)
            throw new InputMismatchException();
        if (cur >= num) {
            cur = 0;
            try {
                num = stream.read(buf);
            } catch (Exception e) {
                throw new InputMismatchException();
            }
            if (num <= 0)
                return -1;
        }
        return buf[cur++];
    }

    private boolean isdel(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    @Override
    public void close() {
        try {
            stream.close();
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }
}