TPGA  The Permutation Game Again
Since YoMamaSoFat was able to answer Blackhood's and Kira's question as in http://www.spoj.com/problems/TPGAME/ (though with a little help from your side), it was my turn to ask him a question. This would again be a coding question as you might be knowing he is a noob in coding. I gave him a permutation of N distinct integers from 1...N and asked him the rank of the permutation when all possible permutations of the integers are arranged lexicographically. eg for N=3, all possible permutations arranged lexicographically would be:
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
From the above, rank of 1 2 3 would be 1, rank of 1 3 2 would be 2 and so on...
HELP HIM!
NOTE: You may assume it is the same permutation which Blackhood gave him in http://www.spoj.com/problems/TPGAME/ to tell the no. of inversions for each integer in it.
Input
First line of the input contains t, the no. of test cases. (1<=t<=10)
2*t lines follow, two for each test case.
Each test case begins with an integer N , the no of elements in the permutation.(1<=N<=200000)
The next line contains N space separated distinct integers from 1...N, representing the permutation.
Output
For each test case, print the rank of permutation %1000000007 on a new line.
Example
Input:
3
1
1
3
3 2 1
4
2 1 4 3
Output: 1
6
8
hide comments
eulerkochy:
20181214 06:09:24
O(nlogn) works fine..little bit combi+ BIT ! 

akjol2049:
20181205 06:26:53
NlogN TL.. does O(N) solution exist? 

jmr99:
20180719 17:51:39
getting wrong answer again and again !! 

be1035016:
20180625 22:24:12
BaZ Pro;) 

vijayrit:
20170705 22:08:03
Last edit: 20170706 08:05:50 

vijayrit:
20170704 19:56:01
i am getting TLE ;( Please help

Added by:  null 
Date:  20170703 
Time limit:  0s0.159s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  Motivated by www.spoj.com/problems/PERMRANK 