|Codeforces Beta Round #57 (Div. 2)|
The Romans have attacked again. This time they are much more than the Persians but Shapur is ready to defeat them. He says: "A lion is never afraid of a hundred sheep".
Nevertheless Shapur has to find weaknesses in the Roman army to defeat them. So he gives the army a weakness number.
In Shapur's opinion the weakness of an army is equal to the number of triplets i, j, k such that i < j < k and a i > a j > a k where a x is the power of man standing at position x. The Roman army has one special trait — powers of all the people in it are distinct.
Help Shapur find out how weak the Romans are.
The first line of input contains a single number n (3 ≤ n ≤ 106) — the number of men in Roman army. Next line contains n different positive integers a i (1 ≤ i ≤ n, 1 ≤ a i ≤ 109) — powers of men in the Roman army.
A single integer number, the weakness of the Roman army.
Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cout (also you may use %I64d).
3 2 1
2 3 1
10 8 3 1
1 5 4 3