Problem:
Score : 400 points

Problem Statement

We have N balls. The i-th ball has an integer A_i written on it.

For each k=1, 2, ..., N, solve the following problem and print the answer.

Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.

Constraints

3 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

For each k=1,2,...,N, print a line containing the answer.

Sample Input 1

5
1 1 2 1 2

Sample Output 1

2
2
3
2
3

Consider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.

From these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.

Thus, the answer for k=1 is 2.

Sample Input 2

4
1 2 3 4

Sample Output 2

0
0
0
0

No two balls have equal numbers written on them.

Sample Input 3

5
3 3 3 3 3

Sample Output 3

6
6
6
6
6

Any two balls have equal numbers written on them.

Sample Input 4

8
1 2 1 4 2 1 4 1

Sample Output 4

5
7
5
7
7
5
7
5

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;
using static ABC159.D.Cin;
using static ABC159.D.Util;
using Pair = ABC159.D.VTuple<long, long>;
using Graph = System.Collections.Generic.List<System.Collections.Generic.List<long>>;
using System.Text;

namespace ABC159
{
    public class D
    {
        public static void Main(string[] args)
        {
            long n = rl;
            long[] a = rla;
            long[] b = new long[200001];
            foreach(var m in a)
            {
                b[m]++;
            }
            long[] acc = Accumulate(b.Select(m => (long)nCk(m, 2)).ToArray());

            DontAutoFlush();
            for (int i = 0; i < n; i++)
            {
                long ans = (acc[a[i]] - acc[0]) + (acc[200000] - acc[a[i]+1]) + (long)nCk(b[a[i]] - 1, 2);
                Console.WriteLine(ans);
            }
            Flush();
        }

        /// <summary>
        /// nが大きくてkが小さいときに使える。
        /// </summary>
        /// <param name="n"></param>
        /// <param name="k"></param>
        /// <returns></returns>
        static Mint nCk(long n, long k)
        {
            Mint x = 1;
            Mint y = 1;
            for (int i = 0; i < k; i++)
            {
                x *= n - i;
                y *= i + 1;
            }
            return x / y;
        }

        public struct Mint : System.IComparable<Mint>, System.IEquatable<Mint>
        {
            public static readonly long MOD = (long)1e9 + 7;

            /// <summary>
            /// 0以上MOD未満の整数
            /// </summary>
            public long Value;

            #region constructor

            public Mint(long val)
            {
                Value = val % MOD;
                if (Value < 0) Value += MOD;
            }

            /// <summary>
            /// 通常のコンストラクタでは、valに対して%オペレータとif文を使って確実に余りを求める。
            /// しかし場合によってはその値をより軽量の処理で算出出来る場合があるため、上記処理を省きたい時がある。
            /// このメソッドでは引数を既に余りを求め終えた数としてMintのインスタンスを作成する。
            /// </summary>
            /// <param name="val"></param>
            /// <returns></returns>
            private static Mint Ctor(long val)
            {
                return new Mint() { Value = val };
            }

            #endregion

            #region operator overload / override

            public static Mint operator +(Mint a, Mint b)
            {
                long res = a.Value + b.Value;
                if (res > MOD) res -= MOD;
                return Ctor(res);
            }
            public static Mint operator -(Mint a, Mint b)
            {
                long res = a.Value - b.Value;
                if (res < 0) res += MOD;
                return Ctor(res);
            }

            public static Mint operator *(Mint a, Mint b)
            {
                long res = a.Value * b.Value;
                if (res > MOD) res %= MOD;
                return Ctor(res);
            }

            public static Mint operator /(Mint a, Mint b)
            {
                return a * Inv(b);
            }

            public override bool Equals(object obj)
            {
                return obj is Mint && Value == ((Mint)obj).Value;
            }

            public override int GetHashCode()
            {
                return Value.GetHashCode();
            }

            public override string ToString()
            {
                return Value.ToString();
            }

            public static implicit operator Mint(long a) { return new Mint(a); }
            public static explicit operator long(Mint a) { return a.Value; }

            #endregion

            #region public method

            public static Mint Pow(Mint a, long n)
            {
                if (n == 0) return new Mint(1);
                Mint b = Pow(a, n >> 1);
                b *= b;
                if ((n & 1) == 1) b *= a;
                return b;
            }

            public static Mint Inv(Mint n)
            {
                long a = n.Value;
                long b = MOD;

                long x = 1;
                long u = 0;
                while (b != 0)
                {
                    long k = a / b;
                    long _x = u;
                    u = x - k * u;
                    x = _x;

                    long _a = a;
                    a = b;
                    b = _a - (k * b);
                }

                return new Mint(x);
            }

            #endregion

            #region interface implementation

            /// <summary>
            /// 構造体の場合は同値性判断をするEqualsが自動で実装されるが、
            /// それはリフレクションを用いた実装なのでIEquatableを自分で実装したほうが早い。
            /// </summary>
            /// <param name="other"></param>
            /// <returns></returns>
            bool System.IEquatable<Mint>.Equals(Mint other)
            {
                return Value == other.Value;
            }

            int System.IComparable<Mint>.CompareTo(Mint other)
            {
                return Comparer<long>.Default.Compare(Value, other.Value);
            }

            #endregion
        }

        public struct VTuple<T1,T2>:System.IComparable<VTuple<T1,T2>>,System.IEquatable<VTuple<T1,T2>>{public T1 First;public T2 Second;public VTuple(T1 a,T2 b){First=a;Second=b;}public int CompareTo(VTuple<T1,T2>a){int b=Comparer<T1>.Default.Compare(First,a.First);if(b!=0)return b;return Comparer<T2>.Default.Compare(Second,a.Second);}public override bool Equals(object a){return a is VTuple<T1,T2>&&Equals((VTuple<T1,T2>)a);}public bool Equals(VTuple<T1,T2>a){return EqualityComparer<T1>.Default.Equals(First,a.First)&&EqualityComparer<T2>.Default.Equals(Second,a.Second);}public override int GetHashCode(){int a=First!=null?First.GetHashCode():0;int b=Second!=null?Second.GetHashCode():0;uint c=((uint)a<<5)|((uint)a>>27);return((int)c+a)^b;}}public class HashMap<K,V>:System.Collections.Generic.Dictionary<K,V>{V i;static Func<V>j=System.Linq.Expressions.Expression.Lambda<Func<V>>(System.Linq.Expressions.Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public readonly static int[]DXY4={0,1,0,-1,0};public readonly static int[]DXY8={1,1,0,1,-1,0,-1,-1,1};public static void DontAutoFlush(){var a=new System.IO.StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static int ri{get{return ReadInt();}}public static int[]ria{get{return ReadIntArray();}}public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static string[]rsa{get{return ReadStringArray();}}public static int ReadInt(){return int.Parse(i());}public static long ReadLong(){return long.Parse(i());}public static double ReadDouble(){return double.Parse(i());}public static string ReadString(){return i();}public static int[]ReadIntArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){g=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static string[]ReadStringArray(){g=null;return Console.ReadLine().Split(' ');}public static void ReadCol(out long[]a,long b){a=new long[b];for(int c=0;c<b;c++)a[c]=ReadLong();}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[,]ReadIntTable(int a,int b){g=null;int[,]c=new int[a,b];for(int d=0;d<a;d++)for(int e=0;e<b;e++){c[d,e]=ReadInt();}return c;}public static long[,]ReadLongTable(long a,long b){g=null;long[,]c=new long[a,b];for(int d=0;d<a;d++)for(int e=0;e<b;e++){c[d,e]=ReadLong();}return c;}public static char[,]ReadCharTable(int a,int b){g=null;char[,]c=new char[a,b];for(int d=0;d<a;d++){var e=ReadString();for(int f=0;f<b;f++)c[d,f]=e[f];}return c;}static string[]g;static int h;static string i(){if(g==null||g.Length<=h){g=Console.ReadLine().Split(' ');h=0;}return g[h++];}}
    }
}