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
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 1/7/20

"""

import collections
import time
import os
import sys
import bisect
import heapq
from typing import List



def solve(N, A):
    
    B = list(sorted(set(A)))
    vi = {v: i for i, v in enumerate(B)}
    A = [vi[v] for v in A]
    
    wc = collections.defaultdict(int)
    precount = [0 for _ in range(N)]
    for i, v in enumerate(A):
        wc[v] += 1
        precount[i] = wc[v]
    
    
        
    
    wc = collections.defaultdict(int)
    sufcount = []
    for v in reversed(A):
        wc[v] += 1
        sufcount.append(wc[v])
    sufcount = sufcount[::-1]

    bit = [0 for _ in range(N)]

    def add(index, val):
        while index < N:
            bit[index] += val
            index |= index + 1

    def query(index):
        s = 0
        while index >= 0:
            s += bit[index]
            index = (index & (index + 1)) - 1
        return s

    ans = 0
    for i in range(N - 2, -1, -1):
        v = precount[i]
        add(sufcount[i+1], 1)
        ans += query(v-1)
                
    return ans
    

N = int(input())
A = [int(x) for x in input().split()]
print(solve(N, A))