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.util.HashMap;
import java.util.Scanner;
 
public class P459D {
 
	private static int n;
	private static int[] a;
	private static int[] seg;
	private static int m;
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		n = in.nextInt();
		a = new int[n];
		for(int i=0; i<n; i++) {
			a[i] = in.nextInt();
		}
		
		HashMap<Integer, Integer> set = new HashMap<>();
		int[] left = new int[n];
		for(int i=0; i<n; i++) {
			set.put(a[i], set.getOrDefault(a[i], 0)+1);
			left[i] = set.get(a[i]);
		}
		set.clear();
		int[] right = new int[n];
		for(int i=n-1; i>=0; i--) {
			set.put(a[i], set.getOrDefault(a[i], 0)+1);
			right[i] = set.get(a[i]);
		}
		long ans=0;
		m = 2*(int)Math.pow(2, Math.ceil(Math.log10(n+1)/Math.log10(2)))-1;
		seg = new int[m];
		for(int i=n-1; i>=0; i--) {
			ans += get(0, left[i]-1, 0, n, 0);
			update(right[i], 1);
		}
		System.out.println(ans);
 
	}
	
	private static void update(int i, int v) {
		int k = index(i, 0, n, 0);
		seg[k] += v;  
		while(k>0) {
			k = (k-1)/2;
			seg[k] = seg[2*k+1]+seg[2*k+2];
		}
	}
	
	private static int get(int qlow, int qhigh, int low, int high, int pos) {
		if (qlow>qhigh) {
			return 0;
		}
		if (qhigh<low || high<qlow) {
			return 0;
		} else if (qlow<=low && qhigh>=high) {
			return seg[pos];
		} else {
			int mid = (low+high)/2;
			return get(qlow, qhigh, low, mid, 2*pos+1)+get(qlow, qhigh, mid+1, high, 2*pos+2);
		}	
	}
	
	private static int index(int i, int low, int high, int pos) {
		if (low==high) {
			return pos;
		}
		
		int mid = (low+high)/2;
		if (i<=mid) {
			return index(i, low, mid, 2*pos+1);
		} else {
			return index(i, mid+1, high, 2*pos+2);
		}
	}
}
