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    Minimum Inversion Number

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
    Total Submission(s): 29690    Accepted Submission(s): 16982


    Problem Description
    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
     

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