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#F1937. Pashmak and Parmida's problem

    ID: 1943 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 5 上传者: 标签>数据结构分治排序算法思想编程与模拟进阶难度共享题库Codeforces英文题面题目来源题面语言

Pashmak and Parmida's problem

题目描述

D. Pashmak and Parmida's problem
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1517 题。保留原作者与原赛事署名。