BalanceString←{
     let←¯1 ⎕C ⎕A
     dig←⎕D
     BS←{
         sorted←⍵[⍋⍵]
         l←sorted∊let ⋄ d←sorted∊dig
         1<|l-⍥(+/)d:''
         mo←⍒(l×+/l)+(d×+/d)
         Ignore0←(⌊/⍬)@(0∘=)
         o←sorted[mo]
         o[⍋(+\o∊let)⌊⍥Ignore0(+\o∊dig)]
     }

⍝ Tests
     '0a1b2c'≢BS'a0b1c2':∘∘∘
     'a1b2c'≢BS'abc12':∘∘∘
     '0a1b2c3'≢BS'0a2b1c3':∘∘∘
     ''≢BS'1a23':∘∘∘
     '1a2b3'≢BS'ab123':∘∘∘

     'All tests passed.'
 }