LCMSUM - LCM Sum


Given n, calculate the sum LCM(1, n) + LCM(2, n) + .. + LCM(n, n), where LCM(i, n) denotes the Least Common Multiple of the integers i and n.

Input

The first line contains T the number of test cases. Each of the next T lines contain an integer n.

Output

Output T lines, one for each test case, containing the required sum.

Example

Input:
3
1
2
5

Output:
1
4
55

Constraints

1 ≤ T ≤ 300000
1 ≤ n ≤ 1000000


hide comments
vaibhav goyal: 2016-07-08 16:59:03

scanf is also giving tle's
finally got ac by fast i/o
nice problem :)

ritik_agr: 2016-07-04 05:39:57

learnt new concepts from this problem

Last edit: 2016-07-04 05:40:16
sanghpriya785: 2015-10-06 13:41:37

getting tle in c as well as in python also.
but learn a lot

Infinity: 2014-11-03 12:02:03

interesting problem.Had to refer the web to get the first idea.

Last edit: 2014-11-03 13:05:20
pankaj: 2014-10-23 08:50:15

final AC

Bhavik: 2014-02-16 19:20:51

learnt something new..:)

Last edit: 2014-02-16 19:21:14
adhikari vushesh babu: 2013-09-20 20:53:58

At last green light :)
use scanf and printf instead of cin and cout which costed me many TLE.

Ouditchya Sinha: 2013-04-29 08:40:16

Great Problem! Learnt a lot about totient function... But I think there's some server instability, my earlier solution ran in 4.19s on ideone & here it TLE'd, my improved solution ran in 0.42s on ideone & here it took 4.13s. Strange. :)

Rajarshi Sarkar: 2013-04-29 06:55:43

One does not simply calculate LCM :D

saket diwakar: 2013-01-30 23:14:57

finally got AC....:)
same algo getting TLE in python..#strange

Last edit: 2013-01-30 23:16:40

Added by:Varun Jalan
Date:2010-01-24
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: PERL6
Resource:own problem used for Codechef Snackdown Onsite