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).