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
from sys import stdin, stdout
from collections import Counter, defaultdict
from itertools import permutations, combinations
raw_input = stdin.readline
pr = stdout.write
mod=10**9+7

def ni():
    return int(raw_input())


def li():
    return map(int,raw_input().split())


def pn(n):
    stdout.write(str(n)+'\n')


def pa(arr):
    pr(' '.join(map(str,arr))+'\n')

# fast read function for total integer input

def inp():
    # this function returns whole input of
    # space/line seperated integers
    # Use Ctrl+D to flush stdin.
    return map(int,stdin.read().split())

range = xrange # not for python 3.0+

#main code

n=ni()
BITTree=[0]*(n+1)
def gs(i): 
    s = 0
    i = i+1
    while i > 0:  
        s += BITTree[i] 
        i -= i & (-i) 
    return s 
def ub(i ,v): 
    i += 1
    while i <= n: 
        BITTree[i] += v 
        i += i & (-i) 

l=li()
l1,l2=[],[]
d=Counter()
for i in range(n-1):
    d[l[i]]+=1
    l1.append(d[l[i]])
d=Counter()
for i in range(n-1,0,-1):
    d[l[i]]+=1
    l2.append(d[l[i]])
ans=0
l1=l1[::-1]
for i in range(n-1):
    ub(l2[i]+1,1)
    ans+=gs(l1[i])
pn(ans)
