Enter size n: Enter vector number 1: Enter vector number 2: Enter vector number 3: Before reduction, vectors are:
[1,2,3]
[4,5,6]
[7,8,8]

FIRST METHOD: JC'S implementation of integer LLL from HC's book
After reduction, vectors are:
[0,0,-1]
[-1,1,0]
[1,2,0]

Square length of vector 1 is 1
Square length of vector 2 is 2
Square length of vector 3 is 5
Candidates for shortest vectors:
(1,1,1): [0,3,-1], norm = 10
(1,1,0): [-1,1,-1], norm = 3
(1,1,-1): [-2,-1,-1], norm = 6
(1,0,1): [1,2,-1], norm = 6
(1,0,0): [0,0,-1], norm = 1
(1,0,-1): [-1,-2,-1], norm = 6
(1,-1,1): [2,1,-1], norm = 6
(1,-1,0): [1,-1,-1], norm = 3
(1,-1,-1): [0,-3,-1], norm = 10
(0,1,1): [0,3,0], norm = 9
(0,1,0): [-1,1,0], norm = 2
(0,1,-1): [-2,-1,0], norm = 5
(0,0,1): [1,2,0], norm = 5
The shortest vector is [0,0,-1] with square length 1