D. Pashmak and Parmida's problemtime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputParmida 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.InputThe 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).OutputPrint a single integer — the answer to the problem.ExamplesInput71 2 1 1 2 2 1Output8Input31 1 1Output1Input51 2 3 4 5Output0
Input71 2 1 1 2 2 1
Output8
['data structures', 'divide and conquer', 'sortings', '*1800']