Largest LCM

Time Limit: 1 sec

 

The Problem

Given N, print the largest LCM (Least Common Multiple) of any two i and j where 1 ≤ i, j ≤ N.

 

For example if N=4 then

LCM(1,1)=1, LCM(1,2)=2, LCM(1,3)=3, LCM(1,4)=4,

LCM(2,1)=2, LCM(2,2)=2, LCM(2,3)=6, LCM(2,4)=4,

LCM(3,1)=3, LCM(3,2)=6, LCM(3,3)=3, LCM(3,4)=12,

LCM(4,1)=4, LCM(4,2)=4, LCM(4,3)=12, LCM(4,4)=4

So, the largest LCM of pairs of numbers between 1 and 4 is 12.

 

The Input

First line of input will contain the number of test cases, T ≤ 1000. Then T cases follow. For each case, there is a line containing one integer N where 1 ≤ N ≤ 10^5.

 

The Output

For each case, print one line containing a single integer which is the largest LCM of all pairs of numbers between 1 and N.

 

Sample Input

2

2

4

 

Sample Output

2

12

 

 

 

[University Level]

1st Online Programming Contest 2016 by Outsbook

Problem Setter: Shahin ShamS