# Simple MATH answer grader used identically for every arm (last \boxed{}, string normalization, then exact SymPy check of simple numbers).
import re
def last_boxed(t):
    i = t.rfind('\\boxed')
    if i < 0: i = t.rfind('\\fbox')
    if i < 0: return None
    j = t.find('{', i)
    if j < 0: return None
    d = 0
    for k in range(j, len(t)):
        if t[k] == '{': d += 1
        elif t[k] == '}':
            d -= 1
            if d == 0: return t[j+1:k]
    return None
def norm(s):
    if s is None: return None
    s = s.strip()
    s = re.sub(r'\\text\{\s*([^{}]*)\}', r'\1', s)
    for a, b in [('\\left', ''), ('\\right', ''), ('\\!', ''), ('\\,', ''), ('\\;', ''), ('\\ ', ''), ('dfrac', 'frac'), ('tfrac', 'frac'),
                 ('^\\circ', ''), ('^{\\circ}', ''), ('\\%', ''), ('%', ''), ('\\$', ''), ('$', ''), ('\\displaystyle', '')]:
        s = s.replace(a, b)
    s = re.sub(r'\s+', '', s).rstrip('.')
    s = re.sub(r'^[a-z]=', '', s)
    s = re.sub(r'\\frac(\d)(\d)', r'\\frac{\1}{\2}', s)
    s = re.sub(r'\\sqrt(\d)', r'\\sqrt{\1}', s)
    if re.fullmatch(r'-?\d{1,3}(,\d{3})+', s): s = s.replace(',', '')
    s = re.sub(r'(\d)\.0+$', r'\1', s)
    return s
def num(s):
    m = re.fullmatch(r'(-?)\\frac\{(-?\d+)\}\{(\d+)\}', s)
    if m: return (-1 if m.group(1) else 1) * int(m.group(2)) / int(m.group(3))
    try: return float(s)
    except: return None
def correct(text, gold):
    p, g = norm(last_boxed(text)), norm(gold)
    if p is None: return False
    if p == g: return True
    a, b = num(p), num(g)
    return a is not None and b is not None and abs(a - b) < 1e-9