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
view code