import json

def jsonish(text: str) -> dict:
    """
    Convert a JSON-like string (possibly containing invalid escapes and line breaks) to a valid JSON string.
    Process through a state machine: only handle line breaks and invalid escapes within strings.
    """
    valid_escapes = '"\\/bfnrtu'  # JSON valid escape characters
    in_string = False
    escape_active = False
    result_chars = []
    
    for char in text.strip():
        if not in_string:
            # Direct copy outside string
            result_chars.append(char)
            if char == '"':
                in_string = True  # Enter string area
        else:
            if escape_active:
                # Handle escape sequences
                if char in valid_escapes:
                    result_chars.append(char)
                else:
                    result_chars.append('\\')  # Invalid escape: add extra backslash
                    result_chars.append(char)
                escape_active = False
            else:
                if char == '\\':
                    escape_active = True  # Mark escape start
                    result_chars.append(char)
                elif char == '"':
                    in_string = False  # Exit string area
                    result_chars.append(char)
                else:
                    # Line break in string is converted to escape sequence
                    if char == '\n':
                        result_chars.append('\\n')
                    else:
                        result_chars.append(char)
    
    fixed_text = ''.join(result_chars)
    return fixed_text


if __name__ == "__main__":
    # test data (Note: The string contains real line breaks and invalid escapes)
    text = '''{\n  "code": "from sympy import symbols, Eq, solve\\n\\n# define the variables\\nx, y = symbols(\\'x y\\')\\n\\n# define the equations\\neq1 = Eq(2*x + 5*y, 4)\\neq2 = Eq(x + y, 7)\\n\\n# solve the second equation for x\\nsol_y = solve(eq2, y)[0]\\n\\n# substitute the solution of y in the first equation\\neq1_sub = eq1.subs(y, sol_y)\\n\\n# solve the substituted equation\\nsol_x = solve(eq1_sub, x)[0]\\n\\n# solve the equation for y\\nsol = solve(eq2.subs(x, sol_x), y)\\n\\n{\\'x\\': sol_x, \\'y\\': sol[\\'y\\']}"\n}'''

    data = json.loads(jsonish(text))
    print(data)  # Successfully parsed dictionary
