Considering N numbers n, give for each n the sum of the factorials fo the numbers 1 to n :

S(n) = 1! + 2! + 3! + ... + (n-1)! + n!

Input

• 50 ≤ N ≤ 100
• 1000 ≤ n ≤ 3000

Examples

Input :

10
13
20

Output :

4037913
6749977113
2561327494111820313