Codeforces Beta Round 57 (Div. 2) |
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Finished |

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data structures

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E. Enemy is weak

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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).

Examples

Input

3

3 2 1

Output

1

Input

3

2 3 1

Output

0

Input

4

10 8 3 1

Output

4

Input

4

1 5 4 3

Output

1

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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