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
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class CF {
    FastScanner in;
    PrintWriter out;

    class Fenwick {
        int n;
        int[] sum;

        Fenwick(int n) {
            this.n = n;
            sum = new int[n];
        }

        int get(int r) {
            int res = 0;
            for (; r >= 0; r = (r & (r + 1)) - 1)
                res += sum[r];
            return res;
        }

        void add(int r) {
            for (; r < n; r = r | (r + 1))
                sum[r]++;
        }
    }

    void solve() {
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        HashMap<Integer, Integer> cnt = new HashMap<>();
        int[] left = new int[n];
        int[] right = new int[n];
        for (int i = 0; i < n; i++) {
            Integer cur = cnt.get(a[i]);
            if (cur == null)
                cur = 0;
            left[i] = cur++;
            cnt.put(a[i], cur);
        }
        cnt.clear();
        for (int i = n - 1; i >= 0; i--) {
            Integer cur = cnt.get(a[i]);
            if (cur == null)
                cur = 0;
            right[i] = cur++;
            cnt.put(a[i], cur);
        }
        long answer = 0;
        Fenwick f = new Fenwick(n + 5);
        for (int i = n - 1; i >= 0; i--) {
            answer += f.get(left[i] - 1);
            f.add(right[i]);
        }
        out.println(answer);
    }

    void run() {
        try {
            in = new FastScanner(new File("test.in"));
            out = new PrintWriter(new File("test.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

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

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

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

    public static void main(String[] args) {
        new CF().runIO();
    }
}