From bb9c5c30dfd404a05fbf9d86ed68d145d87c67e7 Mon Sep 17 00:00:00 2001
From: blueloveTH <blueloveTH@foxmail.com>
Date: Sun, 2 Jun 2024 23:48:29 +0800
Subject: [PATCH] some fix

---
 python/builtins.py        | 5 +++--
 src/common/_generated.cpp | 2 +-
 2 files changed, 4 insertions(+), 3 deletions(-)

diff --git a/python/builtins.py b/python/builtins.py
index ea3b4caf..aa43489e 100644
--- a/python/builtins.py
+++ b/python/builtins.py
@@ -170,8 +170,9 @@ del __format_string
 def help(obj):
     if hasattr(obj, '__func__'):
         obj = obj.__func__
-    print(obj.__signature__)
-    print(obj.__doc__)
+    # print(obj.__signature__)
+    if obj.__doc__:
+        print(obj.__doc__)
 
 def complex(*args, **kwargs):
     import cmath
diff --git a/src/common/_generated.cpp b/src/common/_generated.cpp
index 3a856096..03dedb9c 100644
--- a/src/common/_generated.cpp
+++ b/src/common/_generated.cpp
@@ -6,7 +6,7 @@ namespace pkpy{
     const char kPythonLibs__long[] = "# after v1.2.2, int is always 64-bit\nPyLong_SHIFT = 60//2 - 1\n\nPyLong_BASE = 2 ** PyLong_SHIFT\nPyLong_MASK = PyLong_BASE - 1\nPyLong_DECIMAL_SHIFT = 4\nPyLong_DECIMAL_BASE = 10 ** PyLong_DECIMAL_SHIFT\n\n##############################################################\n\ndef ulong_fromint(x: int):\n    # return a list of digits and sign\n    if x == 0: return [0], 1\n    sign = 1 if x > 0 else -1\n    if sign < 0: x = -x\n    res = []\n    while x:\n        res.append(x & PyLong_MASK)\n        x >>= PyLong_SHIFT\n    return res, sign\n\ndef ulong_cmp(a: list, b: list) -> int:\n    # return 1 if a>b, -1 if a<b, 0 if a==b\n    if len(a) > len(b): return 1\n    if len(a) < len(b): return -1\n    for i in range(len(a)-1, -1, -1):\n        if a[i] > b[i]: return 1\n        if a[i] < b[i]: return -1\n    return 0\n\ndef ulong_pad_(a: list, size: int):\n    # pad leading zeros to have `size` digits\n    delta = size - len(a)\n    if delta > 0:\n        a.extend([0] * delta)\n\ndef ulong_unpad_(a: list):\n    # remove leading zeros\n    while len(a)>1 and a[-1]==0:\n        a.pop()\n\ndef ulong_add(a: list, b: list) -> list:\n    res = [0] * max(len(a), len(b))\n    ulong_pad_(a, len(res))\n    ulong_pad_(b, len(res))\n    carry = 0\n    for i in range(len(res)):\n        carry += a[i] + b[i]\n        res[i] = carry & PyLong_MASK\n        carry >>= PyLong_SHIFT\n    if carry > 0:\n        res.append(carry)\n    return res\n\ndef ulong_inc_(a: list):\n    a[0] += 1\n    for i in range(len(a)):\n        if a[i] < PyLong_BASE: break\n        a[i] -= PyLong_BASE\n        if i+1 == len(a):\n            a.append(1)\n        else:\n            a[i+1] += 1\n    \n\ndef ulong_sub(a: list, b: list) -> list:\n    # a >= b\n    res = []\n    borrow = 0\n    for i in range(len(b)):\n        tmp = a[i] - b[i] - borrow\n        if tmp < 0:\n            tmp += PyLong_BASE\n            borrow = 1\n        else:\n            borrow = 0\n        res.append(tmp)\n    for i in range(len(b), len(a)):\n        tmp = a[i] - borrow\n        if tmp < 0:\n            tmp += PyLong_BASE\n            borrow = 1\n        else:\n            borrow = 0\n        res.append(tmp)\n    ulong_unpad_(res)\n    return res\n\ndef ulong_divmodi(a: list, b: int):\n    # b > 0\n    res = []\n    carry = 0\n    for i in range(len(a)-1, -1, -1):\n        carry <<= PyLong_SHIFT\n        carry += a[i]\n        res.append(carry // b)\n        carry %= b\n    res.reverse()\n    ulong_unpad_(res)\n    return res, carry\n\n\ndef ulong_divmod(a: list, b: list):\n\n    if ulong_cmp(a, b) < 0:\n        return [0], a\n\n    if len(b) == 1:\n        q, r = ulong_divmodi(a, b[0])\n        r, _ = ulong_fromint(r)\n        return q, r\n\n    max = (len(a) - len(b)) * PyLong_SHIFT + \x5c\n        (a[-1].bit_length() - b[-1].bit_length())\n\n    low = [0]\n\n    high = (max // PyLong_SHIFT) * [0] + \x5c\n        [(2**(max % PyLong_SHIFT)) & PyLong_MASK]\n\n    while ulong_cmp(low, high) < 0:\n        ulong_inc_(high)\n        mid, r = ulong_divmodi(ulong_add(low, high), 2)\n        if ulong_cmp(a, ulong_mul(b, mid)) >= 0:\n            low = mid\n        else:\n            high = ulong_sub(mid, [1])\n\n    q = [0] * (len(a) - len(b) + 1)\n    while ulong_cmp(a, ulong_mul(b, low)) >= 0:\n        q = ulong_add(q, low)\n        a = ulong_sub(a, ulong_mul(b, low))\n    ulong_unpad_(q)\n    return q, a\n\ndef ulong_floordivi(a: list, b: int):\n    # b > 0\n    return ulong_divmodi(a, b)[0]\n\ndef ulong_muli(a: list, b: int):\n    # b >= 0\n    res = [0] * len(a)\n    carry = 0\n    for i in range(len(a)):\n        carry += a[i] * b\n        res[i] = carry & PyLong_MASK\n        carry >>= PyLong_SHIFT\n    if carry > 0:\n        res.append(carry)\n    return res\n\ndef ulong_mul(a: list, b: list):\n    N = len(a) + len(b)\n    # use grade-school multiplication\n    res = [0] * N\n    for i in range(len(a)):\n        carry = 0\n        for j in range(len(b)):\n            carry += res[i+j] + a[i] * b[j]\n            res[i+j] = carry & PyLong_MASK\n            carry >>= PyLong_SHIFT\n        res[i+len(b)] = carry\n    ulong_unpad_(res)\n    return res\n\ndef ulong_powi(a: list, b: int):\n    # b >= 0\n    if b == 0: return [1]\n    res = [1]\n    while b:\n        if b & 1:\n            res = ulong_mul(res, a)\n        a = ulong_mul(a, a)\n        b >>= 1\n    return res\n\ndef ulong_repr(x: list) -> str:\n    res = []\n    while len(x)>1 or x[0]>0:   # non-zero\n        x, r = ulong_divmodi(x, PyLong_DECIMAL_BASE)\n        res.append(str(r).zfill(PyLong_DECIMAL_SHIFT))\n    res.reverse()\n    s = ''.join(res)\n    if len(s) == 0: return '0'\n    if len(s) > 1: s = s.lstrip('0')\n    return s\n\ndef ulong_fromstr(s: str):\n    if s[-1] == 'L':\n        s = s[:-1]\n    res, base = [0], [1]\n    if s[0] == '-':\n        sign = -1\n        s = s[1:]\n    else:\n        sign = 1\n    s = s[::-1]\n    for c in s:\n        c = ord(c) - 48\n        assert 0 <= c <= 9\n        res = ulong_add(res, ulong_muli(base, c))\n        base = ulong_muli(base, 10)\n    return res, sign\n\nclass long:\n    def __init__(self, x):\n        if type(x) is tuple:\n            self.digits, self.sign = x\n        elif type(x) is int:\n            self.digits, self.sign = ulong_fromint(x)\n        elif type(x) is float:\n            self.digits, self.sign = ulong_fromint(int(x))\n        elif type(x) is str:\n            self.digits, self.sign = ulong_fromstr(x)\n        elif type(x) is long:\n            self.digits, self.sign = x.digits.copy(), x.sign\n        else:\n            raise TypeError('expected int or str')\n        \n    def __len__(self):\n        return len(self.digits)\n\n    def __add__(self, other):\n        if type(other) is int:\n            other = long(other)\n        elif type(other) is not long:\n            return NotImplemented\n        if self.sign == other.sign:\n            return long((ulong_add(self.digits, other.digits), self.sign))\n        else:\n            cmp = ulong_cmp(self.digits, other.digits)\n            if cmp == 0:\n                return long(0)\n            if cmp > 0:\n                return long((ulong_sub(self.digits, other.digits), self.sign))\n            else:\n                return long((ulong_sub(other.digits, self.digits), other.sign))\n            \n    def __radd__(self, other):\n        return self.__add__(other)\n    \n    def __sub__(self, other):\n        if type(other) is int:\n            other = long(other)\n        elif type(other) is not long:\n            return NotImplemented\n        if self.sign != other.sign:\n            return long((ulong_add(self.digits, other.digits), self.sign))\n        cmp = ulong_cmp(self.digits, other.digits)\n        if cmp == 0:\n            return long(0)\n        if cmp > 0:\n            return long((ulong_sub(self.digits, other.digits), self.sign))\n        else:\n            return long((ulong_sub(other.digits, self.digits), -other.sign))\n            \n    def __rsub__(self, other):\n        if type(other) is int:\n            other = long(other)\n        elif type(other) is not long:\n            return NotImplemented\n        return other.__sub__(self)\n    \n    def __mul__(self, other):\n        if type(other) is int:\n            return long((\n                ulong_muli(self.digits, abs(other)),\n                self.sign * (1 if other >= 0 else -1)\n            ))\n        elif type(other) is long:\n            return long((\n                ulong_mul(self.digits, other.digits),\n                self.sign * other.sign\n            ))\n        return NotImplemented\n    \n    def __rmul__(self, other):\n        return self.__mul__(other)\n    \n    #######################################################\n    def __divmod__(self, other):\n        if type(other) is int:\n            assert self.sign == 1 and other > 0\n            q, r = ulong_divmodi(self.digits, other)\n            return long((q, 1)), r\n        if type(other) is long:\n            assert self.sign == 1 and other.sign == 1\n            q, r = ulong_divmod(self.digits, other.digits)\n            assert len(other)>1 or other.digits[0]>0\n            return long((q, 1)), long((r, 1))\n        raise NotImplementedError\n\n    def __floordiv__(self, other):\n        return self.__divmod__(other)[0]\n\n    def __mod__(self, other):\n        return self.__divmod__(other)[1]\n\n    def __pow__(self, other: int):\n        assert type(other) is int and other >= 0\n        if self.sign == -1 and other & 1:\n            sign = -1\n        else:\n            sign = 1\n        return long((ulong_powi(self.digits, other), sign))\n    \n    def __lshift__(self, other: int):\n        assert type(other) is int and other >= 0\n        x = self.digits.copy()\n        q, r = divmod(other, PyLong_SHIFT)\n        x = [0]*q + x\n        for _ in range(r): x = ulong_muli(x, 2)\n        return long((x, self.sign))\n    \n    def __rshift__(self, other: int):\n        assert type(other) is int and other >= 0\n        x = self.digits.copy()\n        q, r = divmod(other, PyLong_SHIFT)\n        x = x[q:]\n        if not x: return long(0)\n        for _ in range(r): x = ulong_floordivi(x, 2)\n        return long((x, self.sign))\n    \n    def __neg__(self):\n        return long((self.digits, -self.sign))\n    \n    def __cmp__(self, other):\n        if type(other) is int:\n            other = long(other)\n        elif type(other) is not long:\n            return NotImplemented\n        if self.sign > other.sign:\n            return 1\n        elif self.sign < other.sign:\n            return -1\n        else:\n            return ulong_cmp(self.digits, other.digits)\n        \n    def __eq__(self, other):\n        return self.__cmp__(other) == 0\n    def __lt__(self, other):\n        return self.__cmp__(other) < 0\n    def __le__(self, other):\n        return self.__cmp__(other) <= 0\n    def __gt__(self, other):\n        return self.__cmp__(other) > 0\n    def __ge__(self, other):\n        return self.__cmp__(other) >= 0\n            \n    def __repr__(self):\n        prefix = '-' if self.sign < 0 else ''\n        return prefix + ulong_repr(self.digits) + 'L'\n";
     const char kPythonLibs__set[] = "class 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_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 __builtins import next as __builtins_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\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 = __builtins_next(a)\n        bi = __builtins_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    print(obj.__doc__)\n\ndef complex(*args, **kwargs):\n    import cmath\n    return cmath.complex(*args, **kwargs)\n\ndef long(*args, **kwargs):\n    import _long\n    return _long.long(*args, **kwargs)\n\n\n# builtin exceptions\nclass StackOverflowError(Exception): pass\nclass IOError(Exception): pass\nclass NotImplementedError(Exception): pass\nclass TypeError(Exception): pass\nclass IndexError(Exception): pass\nclass ValueError(Exception): pass\nclass RuntimeError(Exception): pass\nclass ZeroDivisionError(Exception): pass\nclass NameError(Exception): pass\nclass UnboundLocalError(Exception): pass\nclass AttributeError(Exception): pass\nclass ImportError(Exception): pass\nclass AssertionError(Exception): pass\n\nclass KeyError(Exception):\n    def __init__(self, key=...):\n        self.key = key\n        if key is ...:\n            super().__init__()\n        else:\n            super().__init__(repr(key))\n\n    def __str__(self):\n        if self.key is ...:\n            return ''\n        return str(self.key)\n    \n    def __repr__(self):\n        if self.key is ...:\n            return 'KeyError()'\n        return f'KeyError({self.key!r})'\n";
+    const char kPythonLibs_builtins[] = "from __builtins import next as __builtins_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\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 = __builtins_next(a)\n        bi = __builtins_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(*args, **kwargs):\n    import cmath\n    return cmath.complex(*args, **kwargs)\n\ndef long(*args, **kwargs):\n    import _long\n    return _long.long(*args, **kwargs)\n\n\n# builtin exceptions\nclass StackOverflowError(Exception): pass\nclass IOError(Exception): pass\nclass NotImplementedError(Exception): pass\nclass TypeError(Exception): pass\nclass IndexError(Exception): pass\nclass ValueError(Exception): pass\nclass RuntimeError(Exception): pass\nclass ZeroDivisionError(Exception): pass\nclass NameError(Exception): pass\nclass UnboundLocalError(Exception): pass\nclass AttributeError(Exception): pass\nclass ImportError(Exception): pass\nclass AssertionError(Exception): pass\n\nclass KeyError(Exception):\n    def __init__(self, key=...):\n        self.key = key\n        if key is ...:\n            super().__init__()\n        else:\n            super().__init__(repr(key))\n\n    def __str__(self):\n        if self.key is ...:\n            return ''\n        return str(self.key)\n    \n    def __repr__(self):\n        if self.key is ...:\n            return 'KeyError()'\n        return f'KeyError({self.key!r})'\n";
     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_collections[] = "from __builtins import _enable_instance_dict\nfrom 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        _enable_instance_dict(self)\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 False\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 __repr__(self) -> str:\n        return f\"deque({list(self)!r})\"\n\n";
     const char kPythonLibs_colorsys[] = "\"\"\"Conversion functions between RGB and other color systems.\n\nThis modules provides two functions for each color system ABC:\n\n  rgb_to_abc(r, g, b) --> a, b, c\n  abc_to_rgb(a, b, c) --> r, g, b\n\nAll inputs and outputs are triples of floats in the range [0.0...1.0]\n(with the exception of I and Q, which covers a slightly larger range).\nInputs outside the valid range may cause exceptions or invalid outputs.\n\nSupported color systems:\nRGB: Red, Green, Blue components\nYIQ: Luminance, Chrominance (used by composite video signals)\nHLS: Hue, Luminance, Saturation\nHSV: Hue, Saturation, Value\n\"\"\"\n\n# References:\n# http://en.wikipedia.org/wiki/YIQ\n# http://en.wikipedia.org/wiki/HLS_color_space\n# http://en.wikipedia.org/wiki/HSV_color_space\n\n__all__ = [\"rgb_to_yiq\",\"yiq_to_rgb\",\"rgb_to_hls\",\"hls_to_rgb\",\n           \"rgb_to_hsv\",\"hsv_to_rgb\"]\n\n# Some floating point constants\n\nONE_THIRD = 1.0/3.0\nONE_SIXTH = 1.0/6.0\nTWO_THIRD = 2.0/3.0\n\n# YIQ: used by composite video signals (linear combinations of RGB)\n# Y: perceived grey level (0.0 == black, 1.0 == white)\n# I, Q: color components\n#\n# There are a great many versions of the constants used in these formulae.\n# The ones in this library uses constants from the FCC version of NTSC.\n\ndef rgb_to_yiq(r, g, b):\n    y = 0.30*r + 0.59*g + 0.11*b\n    i = 0.74*(r-y) - 0.27*(b-y)\n    q = 0.48*(r-y) + 0.41*(b-y)\n    return (y, i, q)\n\ndef yiq_to_rgb(y, i, q):\n    # r = y + (0.27*q + 0.41*i) / (0.74*0.41 + 0.27*0.48)\n    # b = y + (0.74*q - 0.48*i) / (0.74*0.41 + 0.27*0.48)\n    # g = y - (0.30*(r-y) + 0.11*(b-y)) / 0.59\n\n    r = y + 0.9468822170900693*i + 0.6235565819861433*q\n    g = y - 0.27478764629897834*i - 0.6356910791873801*q\n    b = y - 1.1085450346420322*i + 1.7090069284064666*q\n\n    if r < 0.0:\n        r = 0.0\n    if g < 0.0:\n        g = 0.0\n    if b < 0.0:\n        b = 0.0\n    if r > 1.0:\n        r = 1.0\n    if g > 1.0:\n        g = 1.0\n    if b > 1.0:\n        b = 1.0\n    return (r, g, b)\n\n\n# HLS: Hue, Luminance, Saturation\n# H: position in the spectrum\n# L: color lightness\n# S: color saturation\n\ndef rgb_to_hls(r, g, b):\n    maxc = max(r, g, b)\n    minc = min(r, g, b)\n    sumc = (maxc+minc)\n    rangec = (maxc-minc)\n    l = sumc/2.0\n    if minc == maxc:\n        return 0.0, l, 0.0\n    if l <= 0.5:\n        s = rangec / sumc\n    else:\n        s = rangec / (2.0-maxc-minc)  # Not always 2.0-sumc: gh-106498.\n    rc = (maxc-r) / rangec\n    gc = (maxc-g) / rangec\n    bc = (maxc-b) / rangec\n    if r == maxc:\n        h = bc-gc\n    elif g == maxc:\n        h = 2.0+rc-bc\n    else:\n        h = 4.0+gc-rc\n    # h = (h/6.0) % 1.0\n    h = h / 6.0\n    h = h - int(h)\n    return h, l, s\n\ndef hls_to_rgb(h, l, s):\n    if s == 0.0:\n        return l, l, l\n    if l <= 0.5:\n        m2 = l * (1.0+s)\n    else:\n        m2 = l+s-(l*s)\n    m1 = 2.0*l - m2\n    return (_v(m1, m2, h+ONE_THIRD), _v(m1, m2, h), _v(m1, m2, h-ONE_THIRD))\n\ndef _v(m1, m2, hue):\n    # hue = hue % 1.0\n    hue = hue - int(hue)\n    if hue < ONE_SIXTH:\n        return m1 + (m2-m1)*hue*6.0\n    if hue < 0.5:\n        return m2\n    if hue < TWO_THIRD:\n        return m1 + (m2-m1)*(TWO_THIRD-hue)*6.0\n    return m1\n\n\n# HSV: Hue, Saturation, Value\n# H: position in the spectrum\n# S: color saturation (\"purity\")\n# V: color brightness\n\ndef rgb_to_hsv(r, g, b):\n    maxc = max(r, g, b)\n    minc = min(r, g, b)\n    rangec = (maxc-minc)\n    v = maxc\n    if minc == maxc:\n        return 0.0, 0.0, v\n    s = rangec / maxc\n    rc = (maxc-r) / rangec\n    gc = (maxc-g) / rangec\n    bc = (maxc-b) / rangec\n    if r == maxc:\n        h = bc-gc\n    elif g == maxc:\n        h = 2.0+rc-bc\n    else:\n        h = 4.0+gc-rc\n    # h = (h/6.0) % 1.0\n    h = h / 6.0\n    h = h - int(h)\n    return h, s, v\n\ndef hsv_to_rgb(h, s, v):\n    if s == 0.0:\n        return v, v, v\n    i = int(h*6.0) # XXX assume int() truncates!\n    f = (h*6.0) - i\n    p = v*(1.0 - s)\n    q = v*(1.0 - s*f)\n    t = v*(1.0 - s*(1.0-f))\n    i = i%6\n    if i == 0:\n        return v, t, p\n    if i == 1:\n        return q, v, p\n    if i == 2:\n        return p, v, t\n    if i == 3:\n        return p, q, v\n    if i == 4:\n        return t, p, v\n    if i == 5:\n        return v, p, q\n    # Cannot get here";