Enemy is weak

5000ms

262144K

Description:

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.

Input:

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.

Output:

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).

Sample Input:

3
3 2 1

Sample Output:

Sample Input:

3
2 3 1

Sample Output:

Sample Input:

4
10 8 3 1

Sample Output:

Sample Input:

4
1 5 4 3

Sample Output:

Informação

Provedor Codeforces

Código CF61E