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.util.HashMap;
import java.util.StringTokenizer;

public class CF261_Problem {

	public static void main(String[] args) {
		new CF261_Problem().run();
	}

	public void run() {
		MyScanner in = new MyScanner();

		int N = in.nextInt();

		int[] A = new int[N];
		for (int i = 0; i < N; i++) {
			A[i] = in.nextInt();
		}

		int[] fLeft = new int[N];
		int[] fRight = new int[N];

		// Fill out the f arrays
		// Left
		HashMap<Integer, Integer> nEqual = new HashMap<Integer, Integer>();
		for (int i = 0; i < N; i++) {
			Integer prevCount = nEqual.get(A[i]);
			if (prevCount == null) {
				fLeft[i] = 1;
				nEqual.put(A[i], 1);
			} else {
				fLeft[i] = prevCount + 1;
				nEqual.put(A[i], prevCount + 1);
			}
		}

		// Right
		nEqual.clear();
		for (int i = N - 1; i >= 0; i--) {
			Integer prevCount = nEqual.get(A[i]);
			if (prevCount == null) {
				fRight[i] = 1;
				nEqual.put(A[i], 1);
			} else {
				fRight[i] = prevCount + 1;
				nEqual.put(A[i], prevCount + 1);
			}
		}

		// Count those satisfying the inequality
		long tot = 0;
		BIT bit = new BIT();
		for (int i = N-1; i >= 0; i--) {
			tot += bit.read(fLeft[i]-1);
			bit.update(fRight[i], 1);
		}
		
		System.out.println(tot);
	}

	public 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;
		}

	}

	public class BIT {
		int[] tree = new int[1000001];

		int read(int idx) {
			int sum = 0;
			while (idx > 0) {
				sum += tree[idx];
				idx -= (idx & -idx);
			}
			return sum;
		}

		void update(int idx, int val) {
			while (idx < tree.length) {
				tree[idx] += val;
				idx += (idx & -idx);
			}
		}

	}

}
