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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;
import java.util.TreeMap;
public class A {
	static int n;
	static int [] BIT;
	public static void main(String[] args)throws Throwable {
		MyScanner sc=new MyScanner();
		PrintWriter pw=new PrintWriter(System.out,true);
		
		n=sc.nextInt();
		BIT=new int [n+1];
		int [] a=new int [n];
		for(int i=0;i<n;i++)
			a[i]=sc.nextInt();
		HashMap<Integer, Integer> map=new HashMap<Integer, Integer>();
		int [] f1=new int [n],fn=new int [n];
		for(int i=0;i<n;i++){
			if(map.containsKey(a[i]))
				map.put(a[i], map.get(a[i])+1);
			else
				map.put(a[i], 1);
			f1[i]=map.get(a[i]);
		}
		map.clear();
		for(int i=n-1;i>=0;i--){
			if(map.containsKey(a[i]))
				map.put(a[i], map.get(a[i])+1);
			else
				map.put(a[i], 1);
			fn[i]=map.get(a[i]);
		}
		long ans=0;
		for(int i=0;i<n;i++){
			ans+=get(n)-get(fn[i]);
			add(f1[i], 1);
		}
		
		pw.println(ans);
		pw.flush();
		pw.close();
	}
	
	public static void add(int idx,int val){
		while(idx>0 && idx<=n){
			BIT[idx]+=val;
			idx+=(idx & -idx);
		}
	}
	
	public static int get(int idx){
		int ans=0;
		while(idx>0){
			ans+=BIT[idx];
			idx-=(idx & -idx);
		}
		return ans;
	}
	
	static class MyScanner {
	      BufferedReader br;
	      StringTokenizer st;
	 
	      public MyScanner() {
	         br = new BufferedReader(new InputStreamReader(System.in));
	      }
	 
	      String next() {
	          while (st == null || !st.hasMoreElements()) {
	              try {
	                  st = new StringTokenizer(br.readLine());
	              } catch (IOException e) {
	                  e.printStackTrace();
	              }
	          }
	          return st.nextToken();
	      }
	 
	      int nextInt() {
	          return Integer.parseInt(next());
	      }
	 
	      long nextLong() {
	          return Long.parseLong(next());
	      }
	 
	      double nextDouble() {
	          return Double.parseDouble(next());
	      }
	 
	      String nextLine(){
	          String str = "";
		  try {
		     str = br.readLine();
		  } catch (IOException e) {
		     e.printStackTrace();
		  }
		  return str;
	      }

	   }
}
