Parmida is a clever girl and she wants to participate in Olympiads this year. Of course she wants her partner to be clever too (although he's not)! Parmida has prepared the following test problem for Pashmak.

There is a sequence a that consists of n integers a1, a2, ..., an. Let's denote f(l, r, x) the number of indices k such that: l ≤ k ≤ r and ak = x. His task is to calculate the number of pairs of indicies i, j (1 ≤ i < j ≤ n) such that f(1, i, ai) > f(j, n, aj).

Help Pashmak with the test.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 106). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print a single integer — the answer to the problem.

Examples

Input

7
1 2 1 1 2 2 1


Output

8


Input

3
1 1 1


Output

1


Input

5
1 2 3 4 5


Output

0
// Author @ BlackRise :) //
// Birla Institute of Technology, Mesra//
import java.io.*;
import java.util.*;

public class pashmakProblem {

    static int BIT[];

    static void Blackrise() {                                                //The name Blackrise is my pen name... you can change the name according to your wish

        int n=ni();
        int ar[]=new int[n];
        HashMap<Integer,Integer> map=new HashMap<>();
        int pre_1_to_i[]=new int[n];
        int suf_j_to_n[]=new int[n];
        BIT=new int[2000005];
        tsc();                                                               //calculates the starting time of execution

        for(int i=0;i<n;i++)
        {
            ar[i]=ni();
            if(map.containsKey(ar[i]))map.put(ar[i],map.get(ar[i])+1);
            else map.put(ar[i],1);
            pre_1_to_i[i]=map.get(ar[i]);
        }
        map.clear();
        long res=0;
        for(int i=n-1;i>=0;i--)
        {
            //pl(i);
            if(map.containsKey(ar[i]))map.put(ar[i],map.get(ar[i])+1);
            else map.put(ar[i],1);
            //pl(map.get(ar[i]));
            suf_j_to_n[i]=map.get(ar[i]);
            res+=result(pre_1_to_i[i]-1);

            update(suf_j_to_n[i],n);
        }
        pl(res);


        tec();                  //calculates the ending time of execution
        //pwt();                //prints the time taken to execute the program
    }

    static long result(int x)
    {
        long res=0;
        for(int i=x;i>0;i-=i&(-i))res+=BIT[i];
        return res;
    }

    static void update(int x,int n)
    {
        for(int i=x;i<=n;i+=i&(-i))BIT[i]++;
    }

    /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////


    static Calendar ts, te;                                                  //For time calculation
    static int mod9 = (int) 1e9 + 7;
    static Lelo input = new Lelo(System.in);
    static PrintWriter pw = new PrintWriter(System.out, true);


    public static void main(String[] args) {                                 //threading has been used to increase the stack size.

        new Thread(null, null, "BlackRise", 1<<25)  //the last parameter is stack size which is desired,
        {
            public void run() {

                try {
                    Blackrise();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

    static class Lelo {                                              //Lelo class for fast input
        private InputStream ayega;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public Lelo(InputStream ayega) {
            this.ayega = ayega;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = ayega.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    // functions to take input//
    static int ni() {
        return input.nextInt();
    }

    static long nl() {
        return input.nextLong();
    }

    static double nd() {
        return input.nextDouble();
    }

    static String ns() {
        return input.readString();
    }

    //functions to give output
    static void pl() {
        pw.println();
    }

    static void p(Object o) {
        pw.print(o + " ");
    }

    static void pws(Object o){
        pw.print(o+"");
    }

    static void pl(Object o) {
        pw.println(o);
    }

    static void tsc()                                          //calculates the starting time of execution
    {
        ts = Calendar.getInstance();
        ts.setTime(new Date());
    }

    static void tec()                                          //calculates the ending time of execution
    {
        te = Calendar.getInstance();
        te.setTime(new Date());
    }

    static void pwt()                                          //prints the time taken for execution
    {
        pw.printf("\nExecution time was :- %f s\n", (te.getTimeInMillis() - ts.getTimeInMillis()) / 1000.00);
    }
}

