#D8978. Pashmak and Parmida's problem
Pashmak and Parmida's problem
Pashmak and Parmida's problem
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
inputFormat
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).
outputFormat
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
样例
3
1 1 1
1