Problem Description

Among the permutations of length $ N $, determine the lexicographical order of $ a $.

Since the answer can be very large, output the remainder when divided by $ 1,000,000,007 $.

Input Format

None

Output Format

None

Sample Input and Output

Sample Input #1

5
3 1 5 4 2

Sample Output #1

54

Sample Input #2

6
1 2 3 4 5 6

Sample Output #2

1

Sample Input #3

7
7 6 5 4 3 2 1

Sample Output #3

5040

Sample Input #4

20
19 11 10 7 8 9 17 18 20 4 3 15 16 1 5 14 6 2 13 12

Sample Output #4

542869439

Notes/Hints

Constraints

• $1 \leq N \leq 100,000$

见题面 Input 部分

见题面 Output 部分