F=\
lambda s:R(f(re.findall(r'\\\W|\\[a-z]+|\S',s)))
import re
def R(I):
r=[]
for i in I:r+=[' '*(r>[]<re.findall('^[a-z]',i)and'\\'==r[-1][0])+i]
return''.join(r)
def f(s,p=0):
v={'\\sqrt':1,'^':1,'_':1,'\\frac':2}
if[]==s:return
if(t:=s.pop(0))in v:k=f(s,1);yield from[t,*[next(k)for _ in range(v[t])]]
if'{'==t:T=[t,*f(s),'}'];yield R([T[1:-1],T][len(T)>3and p])
if'}'!=t:
if~-(t in v)and'{'!=t:yield t
yield from f(s,p)
print(F('\\sum_{n \\leq r^2} {\\frac{v(n)}{n}} + \\frac1n \\in \{1,2,3\}'))
print(F('\\a{b c}d'))
print(F('\\sqrt{b c}d'))
print(F('\\sqrt{2 2}d'))
print(F('\\sqrt{a}d'))
print(F('\\sqrt{2}d'))
print(F('\\frac{1}{2}'))
print(F('\\frac{12}{3}'))
print(F('\\frac{2}{n}'))
print(F('\\frac{a}{n}'))
print(F('\\frac{a+1}{n}'))
print(F('\\frac{\\frac12}3'))
print(F('\\frac{\\sqrt2}3'))
print(F('\\frac {1} {23}'))
print(F('\\a b'))
print(F('^{a b}'))
print(F('{ab}_{\\log}'))
print(F('{\\sqrt{2}}^2'))
print(F('\\frac{\\frac{\\frac{1}{\\sqrt{x_{1}}}+1}{\\sqrt{x_{2}+1}}+2}{\\sqrt{x_{3}+2}}+3'))
print(F('\\sqrt{\{}'))
print(F('\\frac{1}{\\sqrt{x_{1}}}'))
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