5763: On Sum of Number of Inversions in Permutations
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
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题目描述
D. On Sum of Number of Inversions in Permutations
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given a permutation p. Calculate the total number of inversions in all permutations that lexicographically do not exceed the given one.
As this number can be very large, print it modulo 1000000007 (109+7).
As this number can be very large, print it modulo 1000000007 (109+7).
Input
The first line contains a single integer n (1≤n≤106) − the length of the permutation. The second line contains n distinct integers p1,p2,...,pn (1≤pi≤n).
Output
Print a single number − the answer to the problem modulo 1000000007 (109+7).
Examples
Input
2 2 1
Output
1
Input
3 2 1 3
Output
2
Note
Permutation p of length n is the sequence that consists of n distinct integers, each of them is from 1 to n.
An inversion of permutation p1,p2,...,pn is a pair of indexes (i,j), such that i<j and pi>pj.
Permutation a do not exceed permutation b lexicographically, if either a=b or there exists such number i, for which the following logical condition fulfills:
AND (ai<bi).
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