4-rings or 4-squares puzzle

You are encouraged to solve this task according to the task description, using any language you may know.
Task

Replace       a, b, c, d, e, f,   and
  g        with the decimal
digits   LOW   ───►   HIGH

such that the sum of the letters inside of each of the four large squares add up to
the same sum.

            ╔══════════════╗      ╔══════════════╗
            ║              ║      ║              ║
            ║      a       ║      ║      e       ║
            ║              ║      ║              ║
            ║          ┌───╫──────╫───┐      ┌───╫─────────┐
            ║          │   ║      ║   │      │   ║         │
            ║          │ b ║      ║ d │      │ f ║         │
            ║          │   ║      ║   │      │   ║         │
            ║          │   ║      ║   │      │   ║         │
            ╚══════════╪═══╝      ╚═══╪══════╪═══╝         │
                       │       c      │      │      g      │
                       │              │      │             │
                       │              │      │             │
                       └──────────────┘      └─────────────┘

Show all output here.



   Show all solutions for each letter being unique with
        LOW=1     HIGH=7

   Show all solutions for each letter being unique with
        LOW=3     HIGH=9

   Show only the   number   of solutions when each letter can be non-unique
        LOW=0     HIGH=9



Related task

 Solve the no connection puzzle


550" :woL">:#,_&>00p" :hgiH">:#,_&>1+10p" :)n/y( euqinU">:#,_>~>:4v
v!g03!:\*`\g01\!`\g00:p05:+g03:p04:_$30g1+:10g\`v1g<,+$p02%2_|#`*8<
>>+\30g-!+20g*!*00g\#v_$40g1+:10g\`^<<1g00p03<<<_$55+:,\."snoitul"v
v!`\g00::p07:+g04p06:<^<`\g01:+1g06$<_v#!\g00*!*g02++!-g05<  v"so"<
>\10g\`*\:::30g-!\40g-!+\50g-!+\60g-!  +60g::30g-!\40g-!+\^  >:#,_@
>0g50g.......55+,0vg02+1_80g1+:10g\`!^>>:80p60g+30g-:90p::00g\`!>>v
^9g03g04g06g08g07<_>>0>>^<<*!*g02++!-g07\+!-g06\+!-g05\+!-g04\!-<<\
>>10g\`*\:::::30g-!\40g-!+\50g-!+\60g-!+\70g-!+\80g-!+80g::::30g^^>