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.util.*;
import java.math.*; 

public class Main {
	static class BIT {
		int n;
		int[] tree;
		
		public BIT(int n) {
			this.n = n;
			tree = new int[n + 2];
		}
		
		int read(int i) {
			i++;
			int sum = 0;
			while (i > 0) {
				sum += tree[i];
				i -= i & -i;
			}
			return sum;
		}
		
		void update(int i, int val) {
			i++;
			while (i <= n) {
				tree[i] += val;
				i += i & -i;
			}
		}
	}
	public static void main(String[] args) throws IOException 
	{ 
		FastScanner f = new FastScanner(); 
		int t=1;
//		t=f.nextInt();
		PrintWriter out=new PrintWriter(System.out);
		while(t>0) {
			t--;
			int n=f.nextInt();
			int[] l=f.readArray(n);
			HashMap<Integer,Integer> h=new HashMap<>();
			int[] left=new int[n];
			int[] right=new int[n];
			for(int i=0;i<n;i++) {
				if(h.containsKey(l[i])) {
					h.put(l[i], h.get(l[i])+1);
				}
				else {
					h.put(l[i],1);
				}
				left[i]=h.get(l[i]);
			}
			h.clear();
			for(int i=n-1;i>-1;i--) {
				if(h.containsKey(l[i])) {
					h.put(l[i], h.get(l[i])+1);
				}
				else {
					h.put(l[i],1);
				}
				right[i]=h.get(l[i]);
			}
			int max=1000005;
			BIT bit=new BIT(max);
			long ans=0;
			for(int i=0;i<n;i++) {
				ans+=bit.read(max)-bit.read(right[i]);
				bit.update(left[i],1);
//				for(int j=0;j<bit.tree.length;j++) {
//					System.out.print(bit.tree[i]+" ");
//				}
//				System.out.println();
			}
			System.out.println(ans);
		}
		out.close();
	} 
	static void sort(int [] a) {
        ArrayList<Integer> q = new ArrayList<>();
        for (int i: a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }
    
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		long[] readLongArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}
} 	