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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
using static AtCoder.CalcL;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        //const int MOD = 998244353;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1 };
        static readonly int[] dJ = { 1, 0, -1, 0 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>> G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            int N = int.Parse(Console.ReadLine());
            var a = cin.ReadSplitLong();
            var mx = new long[N];
            mx[0] = a[0];
            for (var i = 1; i < N; i++) mx[i] = Max(mx[i - 1], a[i]);
            var num = new Dictionary<long, long>();
            var ind = new Dictionary<long, int>();
            for(var i = 0; i < N; i++)
            {
                if (num.ContainsKey(a[i]))
                {
                    num[a[i]]++;
                }
                else
                {
                    num[a[i]] = 1;
                    ind[a[i]] = i;
                }
                
            }
            var curmx = a.Max();
            long curnum = a.Count(x => x == curmx);
            int minind = INF;
            for (var i = 0; i < N; i++) { if (a[i] == curmx) { minind = i; break; } }

            var ans = new long[N];
            Initialize(ref ans, 0);
            while (minind > 0)
            {
                long nx = mx[minind - 1];
                ans[minind] += (curmx - nx) * curnum;
                curmx = nx;
                curnum += num[nx];
                minind = ind[nx];
            }
            ans[0] += a.Sum() - ans.Sum();
            Console.WriteLine(string.Join("\n", ans));
            

            //Console.Out.Flush();
        }
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
    }
    public class UnionFind
    {
        private int[] parent;
        private int[] rank;
        private int[] size;
        public UnionFind(int n)
        {
            parent = new int[n];
            rank = new int[n];
            size = new int[n];
            for (var i = 0; i < n; i++)
            {
                parent[i] = i;
                rank[i] = 0;
                size[i] = 1;
            }
        }

        public int Root(int x)
        {
            return parent[x] == x ? x : parent[x] = Root(parent[x]);
        }

        public bool SameRoot(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y) { return; }

            if (rank[x] < rank[y])
            {
                parent[x] = y;
                size[y] += size[x];
                size[x] = 0;
            }
            else
            {
                parent[y] = x;
                if (rank[x] == rank[y]) { rank[x]++; }
                size[x] += size[y];
                size[y] = 0;
            }
        }

        public int SizeOf(int x)
        {
            return size[Root(x)];
        }

    }
    public class Scanner
    {
        public int[] ReadSplitInt()
        {
            return ConvertAll(Console.ReadLine().Split(), int.Parse);
        }
        public long[] ReadSplitLong()
        {
            return ConvertAll(Console.ReadLine().Split(), long.Parse);
        }
        public double[] ReadSplit_Double()
        {
            return ConvertAll(Console.ReadLine().Split(), double.Parse);
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

        static public long LPow(int a, int b)
        {
            return (long)Pow(a, b);
        }
    }
    static public class CalcI
    {
        public static int Gcd(int a, int b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static int Lcm(int a, int b)
        {
            int g = Gcd(a, b);
            return a / g * b;
        }
        public static int Ceil(int n, int div)
        {
            return (n + div - 1) / div;
        }
    }
    static public class CalcL
    {
        public static long Gcd(long a, long b)
        {
            if (a * b == 0) { return Max(a, b); }
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        public static long Lcm(long a, long b)
        {
            long g = Gcd(a, b);
            return a / g * b;
        }
        public static long Ceil(long n, long div)
        {
            return (n + div - 1) / div;
        }
    }
    class Modulo
    {
        private int M;
        private readonly long[] m_facs;
        public long Mul(long a, long b)
        {
            return ((a * b) % M);
        }
        public Modulo(long n, int m)
        {
            M = m;
            m_facs = new long[n + 1];
            m_facs[0] = 1;
            for (long i = 1; i <= n; ++i)
            {
                m_facs[i] = Mul(m_facs[i - 1], i);
            }
        }
        public long Fac(long n)
        {
            return m_facs[n];
        }
        public long Pow(long a, long m)
        {
            switch (m)
            {
                case 0:
                    return 1L;
                case 1:
                    return a;
                default:
                    long p1 = Pow(a, m / 2);
                    long p2 = Mul(p1, p1);
                    return ((m % 2) == 0) ? p2 : Mul(p2, a);
            }
        }
        public long Div(long a, long b)
        {
            return Mul(a, Pow(b, M - 2));
        }
        public long Ncr(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Fac(n);
            res = Div(res, Fac(r));
            res = Div(res, Fac(n - r));
            return res;
        }
    }
}