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 $*n*$ ($3 ≤ *n* ≤ 10^{6}$) — the number of men in Roman army. Next line contains $*n*$ different positive integers $*a*_{*i*}$ ($1 ≤ *i* ≤ *n*, 1 ≤ *a*_{*i*} ≤ 10^{9}$) — 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).