多多的骰子组合

import sys
from collections import defaultdict

def validate_dice(dice):
    """验证骰子的6个面是否包含1到6且不重复"""
    return sorted(dice) == [1, 2, 3, 4, 5, 6]

class Dice:
    def __init__(self, state):
        """初始化骰子状态"""
        if not validate_dice(state):
            raise ValueError("Invalid dice state: must contain numbers 1 to 6 without duplicates.")
        self.state = list(state)
        self.normalize()

    def normalize(self):
        """将骰子标准化：1朝上，最小数朝前"""
        # 将1旋转到上面
        pos_1 = self.state.index(1)
        if pos_1 == 1:
            self._rotate_vertical()
            self._rotate_vertical()
        elif pos_1 == 2:
            self._rotate_vertical()
        elif pos_1 == 3:
            self._rotate_vertical()
            self._rotate_vertical()
            self._rotate_vertical()
        elif pos_1 == 4:
            self._rotate_horizontal()
            self._rotate_vertical()
        elif pos_1 == 5:
            self._rotate_horizontal()
            self._rotate_vertical()
            self._rotate_vertical()
            self._rotate_vertical()

        # 将最小数旋转到前面
        min_number = min(self.state[2:])
        min_number_index = self.state.index(min_number)
        if min_number_index == 3:
            self._rotate_horizontal()
            self._rotate_horizontal()
        elif min_number_index == 4:
            self._rotate_horizontal()
        elif min_number_index == 5:
            self._rotate_horizontal()
            self._rotate_horizontal()
            self._rotate_horizontal()

    def _rotate_vertical(self):
        """绕垂直轴旋转骰子"""
        self.state[0], self.state[1], self.state[2], self.state[3] = (
            self.state[2], self.state[3], self.state[1], self.state[0]
        )

    def _rotate_horizontal(self):
        """绕水平轴旋转骰子"""
        self.state[2], self.state[3], self.state[4], self.state[5] = (
            self.state[4], self.state[5], self.state[3], self.state[2]
        )

def main():
    # 读取输入
    num_dices = int(sys.stdin.readline().strip())
    dices = []
    for _ in range(num_dices):
        dice_state = tuple(map(int, sys.stdin.readline().strip().split()))
        if not validate_dice(dice_state):
            raise ValueError("Invalid dice state: must contain numbers 1 to 6 without duplicates.")
        dices.append(dice_state)

    # 统计骰子类别
    dice_count = defaultdict(int)
    for dice_state in dices:
        dice = Dice(dice_state)
        bottom, right, front = dice.state[1], dice.state[3], dice.state[4]
        dice_count[(bottom, right, front)] += 1

    # 输出结果
    num_categories = len(dice_count)
    counts = sorted(dice_count.values(), reverse=True)
    print(num_categories)
    print(' '.join(map(str, counts)))

if __name__ == "__main__":
    main()

class dice():
    def __init__(self, a):
        self.a=a
    def switch_out(self,i,j):
        if i!=j:
            self.a[2*i], self.a[2*i+1], self.a[2*j], self.a[2*j+1] = \
            self.a[2*j], self.a[2*j+1], self.a[2*i+1], self.a[2*i]
    def switch_in(self,i):
        if self.a[2*i]>self.a[2*i+1]:
            self.a[2*i], self.a[2*i+1] = self.a[2*i+1], self.a[2*i]
            self.a[2*i+2], self.a[2*i+3] = self.a[2*i+3], self.a[2*i+2]
    def tidy(self):
        i1=self.a.index(1)//2
        self.switch_out(0, i1)
        self.switch_in(0)
        i2=self.a.index(min(self.a[2:]))//2
        self.switch_out(1, i2)
        self.switch_in(1)
        return tuple(self.a)
n=int(input())
dc={}
for i in range(n):
    nd=dice(list(map(int, input().split()))).tidy()
    dc[nd]=dc.get(nd, 0)+1
print(len(dc.keys()))
for v in sorted(dc.values(), reverse=True):
    print(v, end=" ")