streem, 318 bytes

Result

AC

Code [DL]

a={case [],s->""
case[x],s->" "+x
case[x,*y],s->x+" "+s+a(y,s)}
j={case[]->""
case[x,*y]->x+j(y)}
stdin|map{x -> j(sort(split(a(split(a(split(a(split(a(split(a(split(a(split(a(split(a(split(a(split(a(split(x,"0"),"0"),"1"),"1"),"2"),"2"),"3"),"3"),"4"),"4"),"5"),"5"),"6"),"6"),"7"),"7"),"8"),"8"),"9"),"9"))))}|stdout

stdin

3445034881266662496441058647497828452778025237468713419893828127816447446830915352033161104487829118

stdout

0000001111111111112222222222333333333444444444444444445555556666666666777777777888888888888888999999

stderr

strace