Each of the letters should be replaced by a different base ten digit from 1 to 9 to satisfy this alphanumeric equation:

  A          D        G
------  +  ------ + ------ = 1, with A > D > G, B > C and, E > F   
 B*C        E*F      HI

Can you solve it, knowing that if I told you whether HIG is a perfect square or not, you would be able to tell me all the other letters?

Note: Each of HI and HIG represents the concatenation of the digits.