diff --git a/src/common/_generated.c b/src/common/_generated.c
index 4baa1c19..0136beff 100644
--- a/src/common/_generated.c
+++ b/src/common/_generated.c
@@ -3,10 +3,10 @@
 #include <string.h>
 const char kPythonLibs__enum[] = "class Enum:\n    def __init__(self, name, value):\n        self.name = name\n        self.value = value\n\n    def __str__(self):\n        return f'{type(self).__name__}.{self.name}'\n    \n    def __repr__(self):\n        return f'<{str(self)}: {self.value!r}>'\n    \n";
 const char kPythonLibs_bisect[] = "\"\"\"Bisection algorithms.\"\"\"\n\ndef insort_right(a, x, lo=0, hi=None):\n    \"\"\"Insert item x in list a, and keep it sorted assuming a is sorted.\n\n    If x is already in a, insert it to the right of the rightmost x.\n\n    Optional args lo (default 0) and hi (default len(a)) bound the\n    slice of a to be searched.\n    \"\"\"\n\n    lo = bisect_right(a, x, lo, hi)\n    a.insert(lo, x)\n\ndef bisect_right(a, x, lo=0, hi=None):\n    \"\"\"Return the index where to insert item x in list a, assuming a is sorted.\n\n    The return value i is such that all e in a[:i] have e <= x, and all e in\n    a[i:] have e > x.  So if x already appears in the list, a.insert(x) will\n    insert just after the rightmost x already there.\n\n    Optional args lo (default 0) and hi (default len(a)) bound the\n    slice of a to be searched.\n    \"\"\"\n\n    if lo < 0:\n        raise ValueError('lo must be non-negative')\n    if hi is None:\n        hi = len(a)\n    while lo < hi:\n        mid = (lo+hi)//2\n        if x < a[mid]: hi = mid\n        else: lo = mid+1\n    return lo\n\ndef insort_left(a, x, lo=0, hi=None):\n    \"\"\"Insert item x in list a, and keep it sorted assuming a is sorted.\n\n    If x is already in a, insert it to the left of the leftmost x.\n\n    Optional args lo (default 0) and hi (default len(a)) bound the\n    slice of a to be searched.\n    \"\"\"\n\n    lo = bisect_left(a, x, lo, hi)\n    a.insert(lo, x)\n\n\ndef bisect_left(a, x, lo=0, hi=None):\n    \"\"\"Return the index where to insert item x in list a, assuming a is sorted.\n\n    The return value i is such that all e in a[:i] have e < x, and all e in\n    a[i:] have e >= x.  So if x already appears in the list, a.insert(x) will\n    insert just before the leftmost x already there.\n\n    Optional args lo (default 0) and hi (default len(a)) bound the\n    slice of a to be searched.\n    \"\"\"\n\n    if lo < 0:\n        raise ValueError('lo must be non-negative')\n    if hi is None:\n        hi = len(a)\n    while lo < hi:\n        mid = (lo+hi)//2\n        if a[mid] < x: lo = mid+1\n        else: hi = mid\n    return lo\n\n# Create aliases\nbisect = bisect_right\ninsort = insort_right\n";
-const char kPythonLibs_builtins[] = "from pkpy import next as __pkpy_next\n\ndef all(iterable):\n    for i in iterable:\n        if not i:\n            return False\n    return True\n\ndef any(iterable):\n    for i in iterable:\n        if i:\n            return True\n    return False\n\ndef enumerate(iterable, start=0):\n    n = start\n    for elem in iterable:\n        yield n, elem\n        n += 1\n\ndef sum(iterable):\n    res = 0\n    for i in iterable:\n        res += i\n    return res\n\ndef map(f, iterable):\n    for i in iterable:\n        yield f(i)\n\ndef filter(f, iterable):\n    for i in iterable:\n        if f(i):\n            yield i\n\ndef zip(a, b):\n    a = iter(a)\n    b = iter(b)\n    while True:\n        ai = __pkpy_next(a)\n        bi = __pkpy_next(b)\n        if ai is StopIteration or bi is StopIteration:\n            break\n        yield ai, bi\n\ndef reversed(iterable):\n    a = list(iterable)\n    a.reverse()\n    return a\n\ndef sorted(iterable, key=None, reverse=False):\n    a = list(iterable)\n    a.sort(key=key, reverse=reverse)\n    return a\n\n##### str #####\ndef __format_string(self: str, *args, **kwargs) -> str:\n    def tokenizeString(s: str):\n        tokens = []\n        L, R = 0,0\n        \n        mode = None\n        curArg = 0\n        # lookingForKword = False\n        \n        while(R<len(s)):\n            curChar = s[R]\n            nextChar = s[R+1] if R+1<len(s) else ''\n            \n            # Invalid case 1: stray '}' encountered, example: \"ABCD EFGH {name} IJKL}\", \"Hello {vv}}\", \"HELLO {0} WORLD}\"\n            if curChar == '}' and nextChar != '}':\n                raise ValueError(\"Single '}' encountered in format string\")        \n            \n            # Valid Case 1: Escaping case, we escape \"{{ or \"}}\" to be \"{\" or \"}\", example: \"{{}}\", \"{{My Name is {0}}}\"\n            if (curChar == '{' and nextChar == '{') or (curChar == '}' and nextChar == '}'):\n                \n                if (L<R): # Valid Case 1.1: make sure we are not adding empty string\n                    tokens.append(s[L:R]) # add the string before the escape\n                \n                \n                tokens.append(curChar) # Valid Case 1.2: add the escape char\n                L = R+2 # move the left pointer to the next char\n                R = R+2 # move the right pointer to the next char\n                continue\n            \n            # Valid Case 2: Regular command line arg case: example:  \"ABCD EFGH {} IJKL\", \"{}\", \"HELLO {} WORLD\"\n            elif curChar == '{' and nextChar == '}':\n                if mode is not None and mode != 'auto':\n                    # Invalid case 2: mixing automatic and manual field specifications -- example: \"ABCD EFGH {name} IJKL {}\", \"Hello {vv} {}\", \"HELLO {0} WORLD {}\" \n                    raise ValueError(\"Cannot switch from manual field numbering to automatic field specification\")\n                \n                mode = 'auto'\n                if(L<R): # Valid Case 2.1: make sure we are not adding empty string\n                    tokens.append(s[L:R]) # add the string before the special marker for the arg\n                \n                tokens.append(\"{\"+str(curArg)+\"}\") # Valid Case 2.2: add the special marker for the arg\n                curArg+=1 # increment the arg position, this will be used for referencing the arg later\n                \n                L = R+2 # move the left pointer to the next char\n                R = R+2 # move the right pointer to the next char\n                continue\n            \n            # Valid Case 3: Key-word arg case: example: \"ABCD EFGH {name} IJKL\", \"Hello {vv}\", \"HELLO {name} WORLD\"\n            elif (curChar == '{'):\n                \n                if mode is not None and mode != 'manual':\n                    # # Invalid case 2: mixing automatic and manual field specifications -- example: \"ABCD EFGH {} IJKL {name}\", \"Hello {} {1}\", \"HELLO {} WORLD {name}\"\n                    raise ValueError(\"Cannot switch from automatic field specification to manual field numbering\")\n                \n                mode = 'manual'\n                \n                if(L<R): # Valid case 3.1: make sure we are not adding empty string\n                    tokens.append(s[L:R]) # add the string before the special marker for the arg\n                \n                # We look for the end of the keyword          \n                kwL = R # Keyword left pointer\n                kwR = R+1 # Keyword right pointer\n                while(kwR<len(s) and s[kwR]!='}'):\n                    if s[kwR] == '{': # Invalid case 3: stray '{' encountered, example: \"ABCD EFGH {n{ame} IJKL {\", \"Hello {vv{}}\", \"HELLO {0} WOR{LD}\"\n                        raise ValueError(\"Unexpected '{' in field name\")\n                    kwR += 1\n                \n                # Valid case 3.2: We have successfully found the end of the keyword\n                if kwR<len(s) and s[kwR] == '}':\n                    tokens.append(s[kwL:kwR+1]) # add the special marker for the arg\n                    L = kwR+1\n                    R = kwR+1\n                    \n                # Invalid case 4: We didn't find the end of the keyword, throw error\n                else:\n                    raise ValueError(\"Expected '}' before end of string\")\n                continue\n            \n            R = R+1\n        \n        \n        # Valid case 4: We have reached the end of the string, add the remaining string to the tokens \n        if L<R:\n            tokens.append(s[L:R])\n                \n        # print(tokens)\n        return tokens\n\n    tokens = tokenizeString(self)\n    argMap = {}\n    for i, a in enumerate(args):\n        argMap[str(i)] = a\n    final_tokens = []\n    for t in tokens:\n        if t[0] == '{' and t[-1] == '}':\n            key = t[1:-1]\n            argMapVal = argMap.get(key, None)\n            kwargsVal = kwargs.get(key, None)\n                                    \n            if argMapVal is None and kwargsVal is None:\n                raise ValueError(\"No arg found for token: \"+t)\n            elif argMapVal is not None:\n                final_tokens.append(str(argMapVal))\n            else:\n                final_tokens.append(str(kwargsVal))\n        else:\n            final_tokens.append(t)\n    \n    return ''.join(final_tokens)\n\nstr.format = __format_string\ndel __format_string\n\n\ndef help(obj):\n    if hasattr(obj, '__func__'):\n        obj = obj.__func__\n    # print(obj.__signature__)\n    if obj.__doc__:\n        print(obj.__doc__)\n\ndef complex(real, imag=0):\n    import cmath\n    return cmath.complex(real, imag)\n\n\nclass set:\n    def __init__(self, iterable=None):\n        iterable = iterable or []\n        self._a = {}\n        self.update(iterable)\n\n    def add(self, elem):\n        self._a[elem] = None\n        \n    def discard(self, elem):\n        self._a.pop(elem, None)\n\n    def remove(self, elem):\n        del self._a[elem]\n        \n    def clear(self):\n        self._a.clear()\n\n    def update(self, other):\n        for elem in other:\n            self.add(elem)\n\n    def __len__(self):\n        return len(self._a)\n    \n    def copy(self):\n        return set(self._a.keys())\n    \n    def __and__(self, other):\n        return {elem for elem in self if elem in other}\n\n    def __sub__(self, other):\n        return {elem for elem in self if elem not in other}\n    \n    def __or__(self, other):\n        ret = self.copy()\n        ret.update(other)\n        return ret\n\n    def __xor__(self, other): \n        _0 = self - other\n        _1 = other - self\n        return _0 | _1\n\n    def union(self, other):\n        return self | other\n\n    def intersection(self, other):\n        return self & other\n\n    def difference(self, other):\n        return self - other\n\n    def symmetric_difference(self, other):      \n        return self ^ other\n    \n    def __eq__(self, other):\n        if not isinstance(other, set):\n            return NotImplemented\n        return len(self ^ other) == 0\n\n    def isdisjoint(self, other):\n        return len(self & other) == 0\n    \n    def issubset(self, other):\n        return len(self - other) == 0\n    \n    def issuperset(self, other):\n        return len(other - self) == 0\n\n    def __contains__(self, elem):\n        return elem in self._a\n    \n    def __repr__(self):\n        if len(self) == 0:\n            return 'set()'\n        return '{'+ ', '.join([repr(i) for i in self._a.keys()]) + '}'\n    \n    def __iter__(self):\n        return iter(self._a.keys())";
-const char kPythonLibs_cmath[] = "import math\n\nclass complex:\n    def __init__(self, real, imag=0):\n        self._real = float(real)\n        self._imag = float(imag)\n\n    @property\n    def real(self):\n        return self._real\n    \n    @property\n    def imag(self):\n        return self._imag\n\n    def conjugate(self):\n        return complex(self.real, -self.imag)\n    \n    def __repr__(self):\n        s = ['(', str(self.real)]\n        s.append('-' if self.imag < 0 else '+')\n        s.append(str(abs(self.imag)))\n        s.append('j)')\n        return ''.join(s)\n    \n    def __eq__(self, other):\n        if type(other) is complex:\n            return self.real == other.real and self.imag == other.imag\n        if type(other) in (int, float):\n            return self.real == other and self.imag == 0\n        return NotImplemented\n    \n    def __add__(self, other):\n        if type(other) is complex:\n            return complex(self.real + other.real, self.imag + other.imag)\n        if type(other) in (int, float):\n            return complex(self.real + other, self.imag)\n        return NotImplemented\n        \n    def __radd__(self, other):\n        return self.__add__(other)\n    \n    def __sub__(self, other):\n        if type(other) is complex:\n            return complex(self.real - other.real, self.imag - other.imag)\n        if type(other) in (int, float):\n            return complex(self.real - other, self.imag)\n        return NotImplemented\n    \n    def __rsub__(self, other):\n        if type(other) is complex:\n            return complex(other.real - self.real, other.imag - self.imag)\n        if type(other) in (int, float):\n            return complex(other - self.real, -self.imag)\n        return NotImplemented\n    \n    def __mul__(self, other):\n        if type(other) is complex:\n            return complex(self.real * other.real - self.imag * other.imag,\n                           self.real * other.imag + self.imag * other.real)\n        if type(other) in (int, float):\n            return complex(self.real * other, self.imag * other)\n        return NotImplemented\n    \n    def __rmul__(self, other):\n        return self.__mul__(other)\n    \n    def __truediv__(self, other):\n        if type(other) is complex:\n            denominator = other.real ** 2 + other.imag ** 2\n            real_part = (self.real * other.real + self.imag * other.imag) / denominator\n            imag_part = (self.imag * other.real - self.real * other.imag) / denominator\n            return complex(real_part, imag_part)\n        if type(other) in (int, float):\n            return complex(self.real / other, self.imag / other)\n        return NotImplemented\n    \n    def __pow__(self, other: int | float):\n        if type(other) in (int, float):\n            return complex(self.__abs__() ** other * math.cos(other * phase(self)),\n                           self.__abs__() ** other * math.sin(other * phase(self)))\n        return NotImplemented\n    \n    def __abs__(self) -> float:\n        return math.sqrt(self.real ** 2 + self.imag ** 2)\n\n    def __neg__(self):\n        return complex(-self.real, -self.imag)\n    \n    def __hash__(self):\n        return hash((self.real, self.imag))\n\n\n# Conversions to and from polar coordinates\n\ndef phase(z: complex):\n    return math.atan2(z.imag, z.real)\n\ndef polar(z: complex):\n    return z.__abs__(), phase(z)\n\ndef rect(r: float, phi: float):\n    return r * math.cos(phi) + r * math.sin(phi) * 1j\n\n# Power and logarithmic functions\n\ndef exp(z: complex):\n    return math.exp(z.real) * rect(1, z.imag)\n\ndef log(z: complex, base=2.718281828459045):\n    return math.log(z.__abs__(), base) + phase(z) * 1j\n\ndef log10(z: complex):\n    return log(z, 10)\n\ndef sqrt(z: complex):\n    return z ** 0.5\n\n# Trigonometric functions\n\ndef acos(z: complex):\n    return -1j * log(z + sqrt(z * z - 1))\n\ndef asin(z: complex):\n    return -1j * log(1j * z + sqrt(1 - z * z))\n\ndef atan(z: complex):\n    return 1j / 2 * log((1 - 1j * z) / (1 + 1j * z))\n\ndef cos(z: complex):\n    return (exp(z) + exp(-z)) / 2\n\ndef sin(z: complex):\n    return (exp(z) - exp(-z)) / (2 * 1j)\n\ndef tan(z: complex):\n    return sin(z) / cos(z)\n\n# Hyperbolic functions\n\ndef acosh(z: complex):\n    return log(z + sqrt(z * z - 1))\n\ndef asinh(z: complex):\n    return log(z + sqrt(z * z + 1))\n\ndef atanh(z: complex):\n    return 1 / 2 * log((1 + z) / (1 - z))\n\ndef cosh(z: complex):\n    return (exp(z) + exp(-z)) / 2\n\ndef sinh(z: complex):\n    return (exp(z) - exp(-z)) / 2\n\ndef tanh(z: complex):\n    return sinh(z) / cosh(z)\n\n# Classification functions\n\ndef isfinite(z: complex):\n    return math.isfinite(z.real) and math.isfinite(z.imag)\n\ndef isinf(z: complex):\n    return math.isinf(z.real) or math.isinf(z.imag)\n\ndef isnan(z: complex):\n    return math.isnan(z.real) or math.isnan(z.imag)\n\ndef isclose(a: complex, b: complex):\n    return math.isclose(a.real, b.real) and math.isclose(a.imag, b.imag)\n\n# Constants\n\npi = math.pi\ne = math.e\ntau = 2 * pi\ninf = math.inf\ninfj = complex(0, inf)\nnan = math.nan\nnanj = complex(0, nan)\n";
+const char kPythonLibs_builtins[] = "from pkpy import next as __pkpy_next\n\ndef all(iterable):\n    for i in iterable:\n        if not i:\n            return False\n    return True\n\ndef any(iterable):\n    for i in iterable:\n        if i:\n            return True\n    return False\n\ndef enumerate(iterable, start=0):\n    n = start\n    for elem in iterable:\n        yield n, elem\n        n += 1\n\ndef sum(iterable):\n    res = 0\n    for i in iterable:\n        res += i\n    return res\n\ndef map(f, iterable):\n    for i in iterable:\n        yield f(i)\n\ndef filter(f, iterable):\n    for i in iterable:\n        if f(i):\n            yield i\n\ndef zip(a, b):\n    a = iter(a)\n    b = iter(b)\n    while True:\n        ai = __pkpy_next(a)\n        bi = __pkpy_next(b)\n        if ai is StopIteration or bi is StopIteration:\n            break\n        yield ai, bi\n\ndef reversed(iterable):\n    a = list(iterable)\n    a.reverse()\n    return a\n\ndef sorted(iterable, key=None, reverse=False):\n    a = list(iterable)\n    a.sort(key=key, reverse=reverse)\n    return a\n\n##### str #####\ndef __format_string(self: str, *args, **kwargs) -> str:\n    def tokenizeString(s: str):\n        tokens = []\n        L, R = 0,0\n        \n        mode = None\n        curArg = 0\n        # lookingForKword = False\n        \n        while(R<len(s)):\n            curChar = s[R]\n            nextChar = s[R+1] if R+1<len(s) else ''\n            \n            # Invalid case 1: stray '}' encountered, example: \"ABCD EFGH {name} IJKL}\", \"Hello {vv}}\", \"HELLO {0} WORLD}\"\n            if curChar == '}' and nextChar != '}':\n                raise ValueError(\"Single '}' encountered in format string\")        \n            \n            # Valid Case 1: Escaping case, we escape \"{{ or \"}}\" to be \"{\" or \"}\", example: \"{{}}\", \"{{My Name is {0}}}\"\n            if (curChar == '{' and nextChar == '{') or (curChar == '}' and nextChar == '}'):\n                \n                if (L<R): # Valid Case 1.1: make sure we are not adding empty string\n                    tokens.append(s[L:R]) # add the string before the escape\n                \n                \n                tokens.append(curChar) # Valid Case 1.2: add the escape char\n                L = R+2 # move the left pointer to the next char\n                R = R+2 # move the right pointer to the next char\n                continue\n            \n            # Valid Case 2: Regular command line arg case: example:  \"ABCD EFGH {} IJKL\", \"{}\", \"HELLO {} WORLD\"\n            elif curChar == '{' and nextChar == '}':\n                if mode is not None and mode != 'auto':\n                    # Invalid case 2: mixing automatic and manual field specifications -- example: \"ABCD EFGH {name} IJKL {}\", \"Hello {vv} {}\", \"HELLO {0} WORLD {}\" \n                    raise ValueError(\"Cannot switch from manual field numbering to automatic field specification\")\n                \n                mode = 'auto'\n                if(L<R): # Valid Case 2.1: make sure we are not adding empty string\n                    tokens.append(s[L:R]) # add the string before the special marker for the arg\n                \n                tokens.append(\"{\"+str(curArg)+\"}\") # Valid Case 2.2: add the special marker for the arg\n                curArg+=1 # increment the arg position, this will be used for referencing the arg later\n                \n                L = R+2 # move the left pointer to the next char\n                R = R+2 # move the right pointer to the next char\n                continue\n            \n            # Valid Case 3: Key-word arg case: example: \"ABCD EFGH {name} IJKL\", \"Hello {vv}\", \"HELLO {name} WORLD\"\n            elif (curChar == '{'):\n                \n                if mode is not None and mode != 'manual':\n                    # # Invalid case 2: mixing automatic and manual field specifications -- example: \"ABCD EFGH {} IJKL {name}\", \"Hello {} {1}\", \"HELLO {} WORLD {name}\"\n                    raise ValueError(\"Cannot switch from automatic field specification to manual field numbering\")\n                \n                mode = 'manual'\n                \n                if(L<R): # Valid case 3.1: make sure we are not adding empty string\n                    tokens.append(s[L:R]) # add the string before the special marker for the arg\n                \n                # We look for the end of the keyword          \n                kwL = R # Keyword left pointer\n                kwR = R+1 # Keyword right pointer\n                while(kwR<len(s) and s[kwR]!='}'):\n                    if s[kwR] == '{': # Invalid case 3: stray '{' encountered, example: \"ABCD EFGH {n{ame} IJKL {\", \"Hello {vv{}}\", \"HELLO {0} WOR{LD}\"\n                        raise ValueError(\"Unexpected '{' in field name\")\n                    kwR += 1\n                \n                # Valid case 3.2: We have successfully found the end of the keyword\n                if kwR<len(s) and s[kwR] == '}':\n                    tokens.append(s[kwL:kwR+1]) # add the special marker for the arg\n                    L = kwR+1\n                    R = kwR+1\n                    \n                # Invalid case 4: We didn't find the end of the keyword, throw error\n                else:\n                    raise ValueError(\"Expected '}' before end of string\")\n                continue\n            \n            R = R+1\n        \n        \n        # Valid case 4: We have reached the end of the string, add the remaining string to the tokens \n        if L<R:\n            tokens.append(s[L:R])\n                \n        # print(tokens)\n        return tokens\n\n    tokens = tokenizeString(self)\n    argMap = {}\n    for i, a in enumerate(args):\n        argMap[str(i)] = a\n    final_tokens = []\n    for t in tokens:\n        if t[0] == '{' and t[-1] == '}':\n            key = t[1:-1]\n            argMapVal = argMap.get(key, None)\n            kwargsVal = kwargs.get(key, None)\n                                    \n            if argMapVal is None and kwargsVal is None:\n                raise ValueError(\"No arg found for token: \"+t)\n            elif argMapVal is not None:\n                final_tokens.append(str(argMapVal))\n            else:\n                final_tokens.append(str(kwargsVal))\n        else:\n            final_tokens.append(t)\n    \n    return ''.join(final_tokens)\n\nstr.format = __format_string\ndel __format_string\n\n\ndef help(obj):\n    if hasattr(obj, '__func__'):\n        obj = obj.__func__\n    # print(obj.__signature__)\n    if obj.__doc__:\n        print(obj.__doc__)\n\ndef complex(real, imag=0):\n    import cmath\n    return cmath.complex(real, imag)\n\n\nclass set:\n    def __init__(self, iterable=None):\n        iterable = iterable or []\n        self._a = {}\n        self.update(iterable)\n\n    def add(self, elem):\n        self._a[elem] = None\n        \n    def discard(self, elem):\n        self._a.pop(elem, None)\n\n    def remove(self, elem):\n        del self._a[elem]\n        \n    def clear(self):\n        self._a.clear()\n\n    def update(self, other):\n        for elem in other:\n            self.add(elem)\n\n    def __len__(self):\n        return len(self._a)\n    \n    def copy(self):\n        return set(self._a.keys())\n    \n    def __and__(self, other):\n        return {elem for elem in self if elem in other}\n\n    def __sub__(self, other):\n        return {elem for elem in self if elem not in other}\n    \n    def __or__(self, other):\n        ret = self.copy()\n        ret.update(other)\n        return ret\n\n    def __xor__(self, other): \n        _0 = self - other\n        _1 = other - self\n        return _0 | _1\n\n    def union(self, other):\n        return self | other\n\n    def intersection(self, other):\n        return self & other\n\n    def difference(self, other):\n        return self - other\n\n    def symmetric_difference(self, other):      \n        return self ^ other\n    \n    def __eq__(self, other):\n        if not isinstance(other, set):\n            return NotImplemented\n        return len(self ^ other) == 0\n    \n    def __ne__(self, other):\n        if not isinstance(other, set):\n            return NotImplemented\n        return len(self ^ other) != 0\n\n    def isdisjoint(self, other):\n        return len(self & other) == 0\n    \n    def issubset(self, other):\n        return len(self - other) == 0\n    \n    def issuperset(self, other):\n        return len(other - self) == 0\n\n    def __contains__(self, elem):\n        return elem in self._a\n    \n    def __repr__(self):\n        if len(self) == 0:\n            return 'set()'\n        return '{'+ ', '.join([repr(i) for i in self._a.keys()]) + '}'\n    \n    def __iter__(self):\n        return iter(self._a.keys())";
+const char kPythonLibs_cmath[] = "import math\n\nclass complex:\n    def __init__(self, real, imag=0):\n        self._real = float(real)\n        self._imag = float(imag)\n\n    @property\n    def real(self):\n        return self._real\n    \n    @property\n    def imag(self):\n        return self._imag\n\n    def conjugate(self):\n        return complex(self.real, -self.imag)\n    \n    def __repr__(self):\n        s = ['(', str(self.real)]\n        s.append('-' if self.imag < 0 else '+')\n        s.append(str(abs(self.imag)))\n        s.append('j)')\n        return ''.join(s)\n    \n    def __eq__(self, other):\n        if type(other) is complex:\n            return self.real == other.real and self.imag == other.imag\n        if type(other) in (int, float):\n            return self.real == other and self.imag == 0\n        return NotImplemented\n    \n    def __ne__(self, other):\n        res = self == other\n        if res is NotImplemented:\n            return res\n        return not res\n    \n    def __add__(self, other):\n        if type(other) is complex:\n            return complex(self.real + other.real, self.imag + other.imag)\n        if type(other) in (int, float):\n            return complex(self.real + other, self.imag)\n        return NotImplemented\n        \n    def __radd__(self, other):\n        return self.__add__(other)\n    \n    def __sub__(self, other):\n        if type(other) is complex:\n            return complex(self.real - other.real, self.imag - other.imag)\n        if type(other) in (int, float):\n            return complex(self.real - other, self.imag)\n        return NotImplemented\n    \n    def __rsub__(self, other):\n        if type(other) is complex:\n            return complex(other.real - self.real, other.imag - self.imag)\n        if type(other) in (int, float):\n            return complex(other - self.real, -self.imag)\n        return NotImplemented\n    \n    def __mul__(self, other):\n        if type(other) is complex:\n            return complex(self.real * other.real - self.imag * other.imag,\n                           self.real * other.imag + self.imag * other.real)\n        if type(other) in (int, float):\n            return complex(self.real * other, self.imag * other)\n        return NotImplemented\n    \n    def __rmul__(self, other):\n        return self.__mul__(other)\n    \n    def __truediv__(self, other):\n        if type(other) is complex:\n            denominator = other.real ** 2 + other.imag ** 2\n            real_part = (self.real * other.real + self.imag * other.imag) / denominator\n            imag_part = (self.imag * other.real - self.real * other.imag) / denominator\n            return complex(real_part, imag_part)\n        if type(other) in (int, float):\n            return complex(self.real / other, self.imag / other)\n        return NotImplemented\n    \n    def __pow__(self, other: int | float):\n        if type(other) in (int, float):\n            return complex(self.__abs__() ** other * math.cos(other * phase(self)),\n                           self.__abs__() ** other * math.sin(other * phase(self)))\n        return NotImplemented\n    \n    def __abs__(self) -> float:\n        return math.sqrt(self.real ** 2 + self.imag ** 2)\n\n    def __neg__(self):\n        return complex(-self.real, -self.imag)\n    \n    def __hash__(self):\n        return hash((self.real, self.imag))\n\n\n# Conversions to and from polar coordinates\n\ndef phase(z: complex):\n    return math.atan2(z.imag, z.real)\n\ndef polar(z: complex):\n    return z.__abs__(), phase(z)\n\ndef rect(r: float, phi: float):\n    return r * math.cos(phi) + r * math.sin(phi) * 1j\n\n# Power and logarithmic functions\n\ndef exp(z: complex):\n    return math.exp(z.real) * rect(1, z.imag)\n\ndef log(z: complex, base=2.718281828459045):\n    return math.log(z.__abs__(), base) + phase(z) * 1j\n\ndef log10(z: complex):\n    return log(z, 10)\n\ndef sqrt(z: complex):\n    return z ** 0.5\n\n# Trigonometric functions\n\ndef acos(z: complex):\n    return -1j * log(z + sqrt(z * z - 1))\n\ndef asin(z: complex):\n    return -1j * log(1j * z + sqrt(1 - z * z))\n\ndef atan(z: complex):\n    return 1j / 2 * log((1 - 1j * z) / (1 + 1j * z))\n\ndef cos(z: complex):\n    return (exp(z) + exp(-z)) / 2\n\ndef sin(z: complex):\n    return (exp(z) - exp(-z)) / (2 * 1j)\n\ndef tan(z: complex):\n    return sin(z) / cos(z)\n\n# Hyperbolic functions\n\ndef acosh(z: complex):\n    return log(z + sqrt(z * z - 1))\n\ndef asinh(z: complex):\n    return log(z + sqrt(z * z + 1))\n\ndef atanh(z: complex):\n    return 1 / 2 * log((1 + z) / (1 - z))\n\ndef cosh(z: complex):\n    return (exp(z) + exp(-z)) / 2\n\ndef sinh(z: complex):\n    return (exp(z) - exp(-z)) / 2\n\ndef tanh(z: complex):\n    return sinh(z) / cosh(z)\n\n# Classification functions\n\ndef isfinite(z: complex):\n    return math.isfinite(z.real) and math.isfinite(z.imag)\n\ndef isinf(z: complex):\n    return math.isinf(z.real) or math.isinf(z.imag)\n\ndef isnan(z: complex):\n    return math.isnan(z.real) or math.isnan(z.imag)\n\ndef isclose(a: complex, b: complex):\n    return math.isclose(a.real, b.real) and math.isclose(a.imag, b.imag)\n\n# Constants\n\npi = math.pi\ne = math.e\ntau = 2 * pi\ninf = math.inf\ninfj = complex(0, inf)\nnan = math.nan\nnanj = complex(0, nan)\n";
 const char kPythonLibs_collections[] = "from typing import Generic, TypeVar, Iterable\n\nT = TypeVar('T')\n\ndef Counter(iterable: Iterable[T]):\n    a: dict[T, int] = {}\n    for x in iterable:\n        if x in a:\n            a[x] += 1\n        else:\n            a[x] = 1\n    return a\n\n\nclass defaultdict(dict):\n    def __init__(self, default_factory, *args):\n        super().__init__(*args)\n        self.default_factory = default_factory\n\n    def __missing__(self, key):\n        self[key] = self.default_factory()\n        return self[key]\n\n    def __repr__(self) -> str:\n        return f\"defaultdict({self.default_factory}, {super().__repr__()})\"\n\n    def copy(self):\n        return defaultdict(self.default_factory, self)\n\n\nclass deque(Generic[T]):\n    _data: list[T]\n    _head: int\n    _tail: int\n    _capacity: int\n\n    def __init__(self, iterable: Iterable[T] = None):\n        self._data = [None] * 8     # initial capacity\n        self._head = 0\n        self._tail = 0\n        self._capacity = len(self._data)\n\n        if iterable is not None:\n            self.extend(iterable)\n\n    def __resize_2x(self):\n        backup = list(self)\n        self._capacity *= 2\n        self._head = 0\n        self._tail = len(backup)\n        self._data.clear()\n        self._data.extend(backup)\n        self._data.extend([None] * (self._capacity - len(backup)))\n\n    def append(self, x: T):\n        self._data[self._tail] = x\n        self._tail = (self._tail + 1) % self._capacity\n        if (self._tail + 1) % self._capacity == self._head:\n            self.__resize_2x()\n\n    def appendleft(self, x: T):\n        self._head = (self._head - 1 + self._capacity) % self._capacity\n        self._data[self._head] = x\n        if (self._tail + 1) % self._capacity == self._head:\n            self.__resize_2x()\n\n    def copy(self):\n        return deque(self)\n    \n    def count(self, x: T) -> int:\n        n = 0\n        for item in self:\n            if item == x:\n                n += 1\n        return n\n    \n    def extend(self, iterable: Iterable[T]):\n        for x in iterable:\n            self.append(x)\n\n    def extendleft(self, iterable: Iterable[T]):\n        for x in iterable:\n            self.appendleft(x)\n    \n    def pop(self) -> T:\n        if self._head == self._tail:\n            raise IndexError(\"pop from an empty deque\")\n        self._tail = (self._tail - 1 + self._capacity) % self._capacity\n        return self._data[self._tail]\n    \n    def popleft(self) -> T:\n        if self._head == self._tail:\n            raise IndexError(\"pop from an empty deque\")\n        x = self._data[self._head]\n        self._head = (self._head + 1) % self._capacity\n        return x\n    \n    def clear(self):\n        i = self._head\n        while i != self._tail:\n            self._data[i] = None\n            i = (i + 1) % self._capacity\n        self._head = 0\n        self._tail = 0\n\n    def rotate(self, n: int = 1):\n        if len(self) == 0:\n            return\n        if n > 0:\n            n = n % len(self)\n            for _ in range(n):\n                self.appendleft(self.pop())\n        elif n < 0:\n            n = -n % len(self)\n            for _ in range(n):\n                self.append(self.popleft())\n\n    def __len__(self) -> int:\n        return (self._tail - self._head + self._capacity) % self._capacity\n\n    def __contains__(self, x: object) -> bool:\n        for item in self:\n            if item == x:\n                return True\n        return False\n    \n    def __iter__(self):\n        i = self._head\n        while i != self._tail:\n            yield self._data[i]\n            i = (i + 1) % self._capacity\n\n    def __eq__(self, other: object) -> bool:\n        if not isinstance(other, deque):\n            return NotImplemented\n        if len(self) != len(other):\n            return False\n        for x, y in zip(self, other):\n            if x != y:\n                return False\n        return True\n    \n    def __ne__(self, other: object) -> bool:\n        if not isinstance(other, deque):\n            return NotImplemented\n        return not self == other\n    \n    def __repr__(self) -> str:\n        return f\"deque({list(self)!r})\"\n\n";
-const char kPythonLibs_datetime[] = "from time import localtime\nimport operator\n\nclass timedelta:\n    def __init__(self, days=0, seconds=0):\n        self.days = days\n        self.seconds = seconds\n\n    def __repr__(self):\n        return f\"datetime.timedelta(days={self.days}, seconds={self.seconds})\"\n\n    def __eq__(self, other: 'timedelta') -> bool:\n        if type(other) is not timedelta:\n            return NotImplemented\n        return (self.days, self.seconds) == (other.days, other.seconds)\n\n    def __ne__(self, other: 'timedelta') -> bool:\n        if type(other) is not timedelta:\n            return NotImplemented\n        return (self.days, self.seconds) != (other.days, other.seconds)\n\n\nclass date:\n    def __init__(self, year: int, month: int, day: int):\n        self.year = year\n        self.month = month\n        self.day = day\n\n    @staticmethod\n    def today():\n        t = localtime()\n        return date(t.tm_year, t.tm_mon, t.tm_mday)\n    \n    def __cmp(self, other, op):\n        if not isinstance(other, date):\n            return NotImplemented\n        if self.year != other.year:\n            return op(self.year, other.year)\n        if self.month != other.month:\n            return op(self.month, other.month)\n        return op(self.day, other.day)\n\n    def __eq__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.eq)\n    \n    def __ne__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.ne)\n\n    def __lt__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.lt)\n\n    def __le__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.le)\n\n    def __gt__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.gt)\n\n    def __ge__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.ge)\n\n    def __str__(self):\n        return f\"{self.year}-{self.month:02}-{self.day:02}\"\n\n    def __repr__(self):\n        return f\"datetime.date({self.year}, {self.month}, {self.day})\"\n\n\nclass datetime(date):\n    def __init__(self, year: int, month: int, day: int, hour: int, minute: int, second: int):\n        super().__init__(year, month, day)\n        # Validate and set hour, minute, and second\n        if not 0 <= hour <= 23:\n            raise ValueError(\"Hour must be between 0 and 23\")\n        self.hour = hour\n        if not 0 <= minute <= 59:\n            raise ValueError(\"Minute must be between 0 and 59\")\n        self.minute = minute\n        if not 0 <= second <= 59:\n            raise ValueError(\"Second must be between 0 and 59\")\n        self.second = second\n\n    def date(self) -> date:\n        return date(self.year, self.month, self.day)\n\n    @staticmethod\n    def now():\n        t = localtime()\n        tm_sec = t.tm_sec\n        if tm_sec == 60:\n            tm_sec = 59\n        return datetime(t.tm_year, t.tm_mon, t.tm_mday, t.tm_hour, t.tm_min, tm_sec)\n\n    def __str__(self):\n        return f\"{self.year}-{self.month:02}-{self.day:02} {self.hour:02}:{self.minute:02}:{self.second:02}\"\n\n    def __repr__(self):\n        return f\"datetime.datetime({self.year}, {self.month}, {self.day}, {self.hour}, {self.minute}, {self.second})\"\n\n    def __cmp(self, other, op):\n        if not isinstance(other, datetime):\n            return NotImplemented\n        if self.year != other.year:\n            return op(self.year, other.year)\n        if self.month != other.month:\n            return op(self.month, other.month)\n        if self.day != other.day:\n            return op(self.day, other.day)\n        if self.hour != other.hour:\n            return op(self.hour, other.hour)\n        if self.minute != other.minute:\n            return op(self.minute, other.minute)\n        return op(self.second, other.second)\n\n    def __eq__(self, other) -> bool:\n        return self.__cmp(other, operator.eq)\n    \n    def __ne__(self, other) -> bool:\n        return self.__cmp(other, operator.ne)\n    \n    def __lt__(self, other) -> bool:\n        return self.__cmp(other, operator.lt)\n    \n    def __le__(self, other) -> bool:\n        return self.__cmp(other, operator.le)\n    \n    def __gt__(self, other) -> bool:\n        return self.__cmp(other, operator.gt)\n    \n    def __ge__(self, other) -> bool:\n        return self.__cmp(other, operator.ge)\n\n\n";
+const char kPythonLibs_datetime[] = "from time import localtime\nimport operator\n\nclass timedelta:\n    def __init__(self, days=0, seconds=0):\n        self.days = days\n        self.seconds = seconds\n\n    def __repr__(self):\n        return f\"datetime.timedelta(days={self.days}, seconds={self.seconds})\"\n\n    def __eq__(self, other: 'timedelta') -> bool:\n        if not isinstance(other, timedelta):\n            return NotImplemented\n        return (self.days, self.seconds) == (other.days, other.seconds)\n\n    def __ne__(self, other: 'timedelta') -> bool:\n        if not isinstance(other, timedelta):\n            return NotImplemented\n        return (self.days, self.seconds) != (other.days, other.seconds)\n\n\nclass date:\n    def __init__(self, year: int, month: int, day: int):\n        self.year = year\n        self.month = month\n        self.day = day\n\n    @staticmethod\n    def today():\n        t = localtime()\n        return date(t.tm_year, t.tm_mon, t.tm_mday)\n    \n    def __cmp(self, other, op):\n        if not isinstance(other, date):\n            return NotImplemented\n        if self.year != other.year:\n            return op(self.year, other.year)\n        if self.month != other.month:\n            return op(self.month, other.month)\n        return op(self.day, other.day)\n\n    def __eq__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.eq)\n    \n    def __ne__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.ne)\n\n    def __lt__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.lt)\n\n    def __le__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.le)\n\n    def __gt__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.gt)\n\n    def __ge__(self, other: 'date') -> bool:\n        return self.__cmp(other, operator.ge)\n\n    def __str__(self):\n        return f\"{self.year}-{self.month:02}-{self.day:02}\"\n\n    def __repr__(self):\n        return f\"datetime.date({self.year}, {self.month}, {self.day})\"\n\n\nclass datetime(date):\n    def __init__(self, year: int, month: int, day: int, hour: int, minute: int, second: int):\n        super().__init__(year, month, day)\n        # Validate and set hour, minute, and second\n        if not 0 <= hour <= 23:\n            raise ValueError(\"Hour must be between 0 and 23\")\n        self.hour = hour\n        if not 0 <= minute <= 59:\n            raise ValueError(\"Minute must be between 0 and 59\")\n        self.minute = minute\n        if not 0 <= second <= 59:\n            raise ValueError(\"Second must be between 0 and 59\")\n        self.second = second\n\n    def date(self) -> date:\n        return date(self.year, self.month, self.day)\n\n    @staticmethod\n    def now():\n        t = localtime()\n        tm_sec = t.tm_sec\n        if tm_sec == 60:\n            tm_sec = 59\n        return datetime(t.tm_year, t.tm_mon, t.tm_mday, t.tm_hour, t.tm_min, tm_sec)\n\n    def __str__(self):\n        return f\"{self.year}-{self.month:02}-{self.day:02} {self.hour:02}:{self.minute:02}:{self.second:02}\"\n\n    def __repr__(self):\n        return f\"datetime.datetime({self.year}, {self.month}, {self.day}, {self.hour}, {self.minute}, {self.second})\"\n\n    def __cmp(self, other, op):\n        if not isinstance(other, datetime):\n            return NotImplemented\n        if self.year != other.year:\n            return op(self.year, other.year)\n        if self.month != other.month:\n            return op(self.month, other.month)\n        if self.day != other.day:\n            return op(self.day, other.day)\n        if self.hour != other.hour:\n            return op(self.hour, other.hour)\n        if self.minute != other.minute:\n            return op(self.minute, other.minute)\n        return op(self.second, other.second)\n\n    def __eq__(self, other) -> bool:\n        return self.__cmp(other, operator.eq)\n    \n    def __ne__(self, other) -> bool:\n        return self.__cmp(other, operator.ne)\n    \n    def __lt__(self, other) -> bool:\n        return self.__cmp(other, operator.lt)\n    \n    def __le__(self, other) -> bool:\n        return self.__cmp(other, operator.le)\n    \n    def __gt__(self, other) -> bool:\n        return self.__cmp(other, operator.gt)\n    \n    def __ge__(self, other) -> bool:\n        return self.__cmp(other, operator.ge)\n\n\n";
 const char kPythonLibs_functools[] = "class cache:\n    def __init__(self, f):\n        self.f = f\n        self.cache = {}\n\n    def __call__(self, *args):\n        if args not in self.cache:\n            self.cache[args] = self.f(*args)\n        return self.cache[args]\n    \ndef reduce(function, sequence, initial=...):\n    it = iter(sequence)\n    if initial is ...:\n        try:\n            value = next(it)\n        except StopIteration:\n            raise TypeError(\"reduce() of empty sequence with no initial value\")\n    else:\n        value = initial\n    for element in it:\n        value = function(value, element)\n    return value\n\nclass partial:\n    def __init__(self, f, *args, **kwargs):\n        self.f = f\n        if not callable(f):\n            raise TypeError(\"the first argument must be callable\")\n        self.args = args\n        self.kwargs = kwargs\n\n    def __call__(self, *args, **kwargs):\n        kwargs.update(self.kwargs)\n        return self.f(*self.args, *args, **kwargs)\n\n";
 const char kPythonLibs_heapq[] = "# Heap queue algorithm (a.k.a. priority queue)\ndef heappush(heap, item):\n    \"\"\"Push item onto heap, maintaining the heap invariant.\"\"\"\n    heap.append(item)\n    _siftdown(heap, 0, len(heap)-1)\n\ndef heappop(heap):\n    \"\"\"Pop the smallest item off the heap, maintaining the heap invariant.\"\"\"\n    lastelt = heap.pop()    # raises appropriate IndexError if heap is empty\n    if heap:\n        returnitem = heap[0]\n        heap[0] = lastelt\n        _siftup(heap, 0)\n        return returnitem\n    return lastelt\n\ndef heapreplace(heap, item):\n    \"\"\"Pop and return the current smallest value, and add the new item.\n\n    This is more efficient than heappop() followed by heappush(), and can be\n    more appropriate when using a fixed-size heap.  Note that the value\n    returned may be larger than item!  That constrains reasonable uses of\n    this routine unless written as part of a conditional replacement:\n\n        if item > heap[0]:\n            item = heapreplace(heap, item)\n    \"\"\"\n    returnitem = heap[0]    # raises appropriate IndexError if heap is empty\n    heap[0] = item\n    _siftup(heap, 0)\n    return returnitem\n\ndef heappushpop(heap, item):\n    \"\"\"Fast version of a heappush followed by a heappop.\"\"\"\n    if heap and heap[0] < item:\n        item, heap[0] = heap[0], item\n        _siftup(heap, 0)\n    return item\n\ndef heapify(x):\n    \"\"\"Transform list into a heap, in-place, in O(len(x)) time.\"\"\"\n    n = len(x)\n    # Transform bottom-up.  The largest index there's any point to looking at\n    # is the largest with a child index in-range, so must have 2*i + 1 < n,\n    # or i < (n-1)/2.  If n is even = 2*j, this is (2*j-1)/2 = j-1/2 so\n    # j-1 is the largest, which is n//2 - 1.  If n is odd = 2*j+1, this is\n    # (2*j+1-1)/2 = j so j-1 is the largest, and that's again n//2-1.\n    for i in reversed(range(n//2)):\n        _siftup(x, i)\n\n# 'heap' is a heap at all indices >= startpos, except possibly for pos.  pos\n# is the index of a leaf with a possibly out-of-order value.  Restore the\n# heap invariant.\ndef _siftdown(heap, startpos, pos):\n    newitem = heap[pos]\n    # Follow the path to the root, moving parents down until finding a place\n    # newitem fits.\n    while pos > startpos:\n        parentpos = (pos - 1) >> 1\n        parent = heap[parentpos]\n        if newitem < parent:\n            heap[pos] = parent\n            pos = parentpos\n            continue\n        break\n    heap[pos] = newitem\n\ndef _siftup(heap, pos):\n    endpos = len(heap)\n    startpos = pos\n    newitem = heap[pos]\n    # Bubble up the smaller child until hitting a leaf.\n    childpos = 2*pos + 1    # leftmost child position\n    while childpos < endpos:\n        # Set childpos to index of smaller child.\n        rightpos = childpos + 1\n        if rightpos < endpos and not heap[childpos] < heap[rightpos]:\n            childpos = rightpos\n        # Move the smaller child up.\n        heap[pos] = heap[childpos]\n        pos = childpos\n        childpos = 2*pos + 1\n    # The leaf at pos is empty now.  Put newitem there, and bubble it up\n    # to its final resting place (by sifting its parents down).\n    heap[pos] = newitem\n    _siftdown(heap, startpos, pos)";
 const char kPythonLibs_itertools[] = "from pkpy import next\n\ndef zip_longest(a, b):\n    a = iter(a)\n    b = iter(b)\n    while True:\n        ai = next(a)\n        bi = next(b)\n        if ai is StopIteration and bi is StopIteration:\n            break\n        if ai is StopIteration:\n            ai = None\n        if bi is StopIteration:\n            bi = None\n        yield ai, bi\n";