function parse( s ){
	delete sl; delete sr
	while(length(s)>0){
		if(match(s,/^[0-9]+/)){
			num[++pindex] = substr(s,RSTART,RLENGTH)
			s = substr(s,RSTART+RLENGTH)
			continue
		}
		else if(s~/^\]/){ # ]
			l = sl[slp--]
			r = pindex
#			print "left",l,"right",r
			num[++pindex] = -1
			ile[pindex] = l
			iri[pindex] = r
			if(slp==0) root = pindex
		}
		else if(s~/^,/){ # ,
			sl[++slp] = pindex
		}
		s = substr(s,2)
	}
}

function cleanparse(s){
	delete ile; delete iri; delete num; delete sl
	slp = 0
	pindex = 0
	parse(s)
}

function parent(id){
	for(i in ile)
		if(ile[i]==id || iri[i]==id) return i
	return -1
}

function levels(id){
	i = id
	count = 0
	if(id==root) return 0
	do{
		i = parent(i)
		if(i<0) return -1
		count++
	}while(i!=root)
	return count
}

function treetostring(id){
	if(num[id]<0)
		return "[" treetostring(ile[id]) "," treetostring(iri[id]) "]"
	else
		return num[id]
}

function leftitemi(id){
	do{
		id--
	}while((num[id]<0 && id>0))
	return id
}

function rightitemi(id){
	do{
		id++
	}while((num[id]<0 && id<=length(num)))
	return id
}


function explode(id){
	lefti = leftitemi(id)
	if(lefti>0){
		num[lefti] += num[id]
		num[id]=-1
	}
	righti = rightitemi(id)
	rightrighti = rightitemi(righti)
	if(rightrighti<=length(num)){
		num[rightrighti] += num[righti]
		num[righti] = -1
	}
	p = parent(id)
	num[p] = 0
}

function toexplode(){
	for(id=1;id<=pindex;id++){
		if((num[id]>=0) && (levels(id)>4) && num[parent(id)]<0) return id
	}
	return -1
}

function dosplit(id){
	n = num[id]
	nl = int(n/2)
	nr = int(n/2) + n%2
	num[id] = -1
	num[++pindex] = nl
	ile[id] = pindex
	num[++pindex] = nr
	iri[id] = pindex
}
function tosplit(){
	for(id=1;id<=pindex;id++){
#		print id, (num[id]-10>0), num[id]
		if((num[id]-10>=0) && num[parent(id)]<0 ) return id
	}
	return -1
}

function reduce(){
	do{
		ind = toexplode()
		print "explode?", ind, num[ind], parent(ind), num[parent(ind)],num[leftitemi(ind)]

		if(ind>0){
			explode(ind)
			print "exploded", treetostring(root)
			s = treetostring(root)
			cleanparse(s)
#			print "to split?",tosplit()
			continue
		}
		ind = tosplit()
		print "split?", ind, num[ind], parent(ind), num[parent(ind)], ile[parent(ind)], iri[parent(ind)]
		if(ind>0){
			dosplit(ind)
			print "split", treetostring(root)
			s = treetostring(root)
			cleanparse(s)
		}
		print toexplode(), tosplit()
	} while( ((toexplode()>0) || (tosplit()>0)) )
	print "done"
}

function magnitude(id){
	if(num[id]>=0) return num[id] # regular number
	# node
	return magnitude(ile[id])*3 + magnitude(iri[id])*2
}

BEGIN{ pindex = 0 }

NR==1{
	parse($0)
	proot = root
}

NR>1{
	parse( $0 )
	num[++pindex] = -1
	ile[pindex] = proot
	iri[pindex] = root
	root = pindex
	print "raw add",NR, treetostring(root)
	reduce()
	s = treetostring(root)
	cleanparse(s)
	proot = root
	print "after",NR,treetostring(root)
}

END{
	OFS=":"
	print pindex, root
#	for(i in num)
#		print i,num[i],levels(i)

#	print "l,r, root:", root
#	for(i in ile)
#		print i, ile[i], iri[i]

#	print num[1], "is at",levels(1),"levels"

	s = treetostring(root)
	cleanparse(s)
	print treetostring(root)

	reduce()

	print treetostring(root)

	print magnitude(root)

}