Minimum Inversion Number

Time Limit: 2 Seconds
Memory Limit: 65536 KB

The inversion number of a given number sequence a1, a2, ..., an is the number
of pairs (ai, aj) that satisfy i < j and ai > aj.

For a given sequence of numbers a1, a2, ..., an, if we move the first m >=
0 numbers to the end of the seqence, we will obtain another sequence. There
are totally n such sequences as the following:

a1, a2, ..., an-1, an (where m = 0 - the initial seqence)

a2, a3, ..., an, a1 (where m = 1)

a3, a4, ..., an, a1, a2 (where m = 2)

...

an, a1, a2, ..., an-1 (where m = n-1)

You are asked to write a program to find the minimum inversion number out of
the above sequences.

**Input**

The input consists of a number of test cases. Each case consists of two lines:
the first line contains a positive integer n (n <= 5000); the next line contains
a permutation of the n integers from 0 to n-1.

Output

For each case, output the minimum inversion number on a single line.

**Sample Input**

10

1 3 6 9 0 8 5 7 4 2

**Sample Output**

16

*
*

Author:

**CHEN, Gaoli**
Source:

**ZOJ Monthly, January 2003**
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