Crazy Thairs
Description
These days, Sempr is crazed on one problem named Crazy Thair. Given N (1 ≤ N ≤ 50000) numbers, which are no more than 109, Crazy Thair is a group of 5 numbers {i, j, k, l, m} satisfying:
1. 1 ≤ i < j < k < l < m ≤ N
2. Ai < Aj < Ak < Al < Am
For example, in the sequence {2, 1, 3, 4, 5, 7, 6},there are four Crazy Thair groups: {1, 3, 4, 5, 6}, {2, 3, 4, 5, 6}, {1, 3, 4, 5, 7} and {2, 3, 4, 5, 7}.
Could you help Sempr to count how many Crazy Thairs in the sequence?
Input
Input contains several test cases. Each test case begins with a line containing a number N, followed by a line containing N numbers.
Output
Output the amount of Crazy Thairs in each sequence.
5
1 2 3 4 5
7
2 1 3 4 5 7 6
7
1 2 3 4 5 6 71
4
21Source
POJ Monthly--2007.09.09, tdzl2003