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from itertools import product, combinations_with_replacement
import time
import threading
from collections import defaultdict
import math
 
# 配置参数（可根据需要修改）
TARGET = 98169  # 目标值
BASE_VALUES = [36.5, 41.5, 59,68.5, 74, 91.5]  # 基础系数列表
FLUCTUATION = 1.0  # 系数波动范围
MAX_SOLUTIONS = 3  # 每个组合的最大解数量
SOLVER_TIMEOUT = 180  # 求解超时时间(秒)
THREE_VAR_THRESHOLD = 220000  # 使用三个变量的阈值
PRODUCT_RANGE_THRESHOLD = 148000  # 乘积范围限制阈值
HIGH_TARGET_THRESHOLD = 260000  # 更高目标值阈值
SHOW_PROGRESS = True  # 是否显示进度
MAX_SOLUTIONS_PER_COMB = 100  # 每个组合的最大解数量，用于提前终止
 
def is_valid_product(p):
    """检查单个乘积是否在有效范围内"""
    if TARGET > PRODUCT_RANGE_THRESHOLD:
        if TARGET > HIGH_TARGET_THRESHOLD:
            return p <= 115000  # 目标值超过260000时，仅限制最大值
        else:
            return 74000 <= p <= 115000  # 目标值在148000-260000之间时，使用原范围
    else:
        return True  # 目标值较小时不限制乘积范围
 
def find_single_variable_solutions(values):
    """查找单个数的解（a*x = TARGET）"""
    solutions = []
    for a in values:
        x = TARGET / a
        if x.is_integer() and 1 <= x <= 10000 and is_valid_product(a * x):
            solutions.append((a, x))
            if len(solutions) >= MAX_SOLUTIONS:
                return solutions  # 提前终止
    return solutions
 
def find_two_variable_solutions(values):
    """查找两个变量的解（a*x + b*y = TARGET）"""
    solutions = defaultdict(list)
 
    # 生成所有可能的(a, b)组合
    for a in values:
        for b in values:
            if a == b:  # 避免重复
                continue
 
            # 计算x的有效范围
            min_x = max(1, math.ceil((TARGET - b * 10000) / a))
            max_x = min(math.floor((TARGET - 1) / a), 10000)
 
            if max_x < min_x:
                continue
 
            for x in range(min_x, max_x + 1):
                remainder = TARGET - a * x
 
                # 检查remainder是否在可能的范围内
                if remainder < 1 or remainder > b * 10000:
                    continue
 
                # 检查remainder是否能被b整除
                if remainder % b == 0:
                    y = remainder // b
                    if 1 <= y <= 10000 and is_valid_product(b * y):
                        solutions[(a, b)].append((a, x, b, y))
                        if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB:
                            break  # 提前终止当前组合的搜索
 
    return solutions
 
def find_three_variable_solutions(values):
    """优化的三变量求解算法"""
    solutions = defaultdict(list)
 
    # 对系数进行排序，便于剪枝
    sorted_values = sorted(values)
 
    # 预计算每个系数的有效范围
    value_ranges = {}
    for a in sorted_values:
        if TARGET > PRODUCT_RANGE_THRESHOLD:
            if TARGET > HIGH_TARGET_THRESHOLD:
                min_x = max(1, math.ceil(1 / a))  # 取消下限，最小为1
                max_x = min(10000, math.floor(115000 / a))
            else:
                min_x = max(1, math.ceil(74000 / a))
                max_x = min(10000, math.floor(115000 / a))
        else:
            min_x = 1
            max_x = 10000
        value_ranges[a] = (min_x, max_x)
 
    total_combinations = len(sorted_values) * (len(sorted_values) - 1) * (len(sorted_values) - 2) // 6
    processed_combinations = 0
 
    # 三重循环，但添加了更多剪枝条件
    for i, a in enumerate(sorted_values):
        min_x, max_x = value_ranges[a]
 
        # 计算可能的x值数量，决定步长
        x_count = max_x - min_x + 1
        x_step = max(1, x_count // 1000)  # 自适应步长
 
        for x in range(min_x, max_x + 1, x_step):
            ax = a * x
            if not is_valid_product(ax):
                continue
 
            remainder1 = TARGET - ax
            if TARGET > PRODUCT_RANGE_THRESHOLD:
                if TARGET > HIGH_TARGET_THRESHOLD:
                    if remainder1 < 0:
                        continue
                else:
                    if remainder1 < 2 * 74000:
                        continue
 
            # 限制b的选择范围，避免重复组合
            for j in range(i + 1, len(sorted_values)):
                b = sorted_values[j]
 
                if TARGET > PRODUCT_RANGE_THRESHOLD:
                    if TARGET > HIGH_TARGET_THRESHOLD:
                        min_y = max(1, math.ceil(1 / b))  # 取消下限，最小为1
                        max_y = min(10000, math.floor(remainder1 / b))
                    else:
                        min_y = max(1, math.ceil(74000 / b))
                        max_y = min(10000, math.floor((remainder1 - 74000) / b))
                else:
                    min_y = 1
                    max_y = math.floor(remainder1 / b)
 
                if max_y < min_y:
                    continue
 
                # 计算可能的y值数量，决定步长
                y_count = max_y - min_y + 1
                y_step = max(1, y_count // 100)  # 自适应步长
 
                for y in range(min_y, max_y + 1, y_step):
                    by = b * y
                    if not is_valid_product(by):
                        continue
 
                    remainder2 = remainder1 - by
                    if TARGET > PRODUCT_RANGE_THRESHOLD:
                        if TARGET > HIGH_TARGET_THRESHOLD:
                            if remainder2 < 0 or remainder2 > 115000:
                                continue
                        else:
                            if remainder2 < 74000 or remainder2 > 115000:
                                continue
 
                    # 限制c的选择范围
                    found_solution = False
                    for k in range(j + 1, len(sorted_values)):
                        c = sorted_values[k]
 
                        # 检查remainder2是否能被c整除
                        if remainder2 % c != 0:
                            continue
 
                        z = remainder2 // c
                        if 1 <= z <= 10000 and is_valid_product(c * z):
                            key = (a, b, c)
                            solutions[key].append((a, x, b, y, c, z))
                            found_solution = True
                            if len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                                break  # 提前终止当前组合的搜索
 
                    # 如果找到解且达到最大数量，跳出y循环
                    if found_solution and len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                        break  # 跳出y循环
 
                # 进度显示
                if SHOW_PROGRESS and j % 10 == 0:
                    print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组", end='')
                processed_combinations += 1
 
    if SHOW_PROGRESS:
        print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组 - 完成")
 
    return solutions
 
def find_balanced_solutions(solutions, var_count, num=2):
    """从所有解中筛选出最平衡的解"""
    if var_count == 1 or not solutions:
        return solutions  # 单变量或无解时直接返回
 
    # 当目标值超过220000时，不计算平衡解
    if TARGET > THREE_VAR_THRESHOLD:
        return []
 
    # 计算解的平衡性（变量间差异最小）
    balanced = []
    for sol in solutions:
        vars = sol[1::2]  # 提取x, y, z
        diff = max(vars) - min(vars)
        balanced.append((diff, sol))
 
    # 按差异排序，取前num个
    return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]]
 
def find_original_solutions(solutions, balanced_solutions, num=3):
    """从剩余解中获取原始顺序的解"""
    if not solutions:
        return []
 
    # 排除已在平衡解中的项
    remaining = [s for s in solutions if s not in balanced_solutions]
    return remaining[:num]
 
def display_solutions(solutions_dict, var_count):
    """优化的解显示函数"""
    if not solutions_dict:
        return
 
    print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解：")
 
    for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1):
        # 当目标值超过220000时，不显示平衡解
        if TARGET > THREE_VAR_THRESHOLD:
            all_display = pair_solutions[:MAX_SOLUTIONS]
            print_tag = "[原始解]"
        else:
            # 计算平衡解和原始解
            balanced = find_balanced_solutions(pair_solutions, var_count)
            original = find_original_solutions(pair_solutions, balanced)
            all_display = balanced + original
 
        if var_count == 1:
            a = coeffs
            print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)")
        elif var_count == 2:
            a, b = coeffs
            print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)")
        else:  # var_count == 3
            a, b, c = coeffs
            print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)")
 
        for j, sol in enumerate(all_display, 1):
            if TARGET > THREE_VAR_THRESHOLD:
                tag = print_tag
            else:
                tag = "[平衡解]" if j <= len(balanced) else "[原始解]"
 
            if var_count == 1:
                a, x = sol
                print(f"  {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}")
            elif var_count == 2:
                a, x, b, y = sol
                print(f"  {j}. x={x}, y={y}, a*x={a*x:.1f}, b*y={b*y:.1f}, 总和={a*x + b*y:.1f} {tag}")
            else:  # var_count == 3
                a, x, b, y, c, z = sol
                print(f"  {j}. x={x}, y={y}, z={z}, "
                      f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, "
                      f"总和={a*x + b*y + c*z:.1f} {tag}")
 
def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT):
    """运行函数并设置超时限制"""
    if kwargs is None:
        kwargs = {}
 
    result = []
    error = []
 
    def wrapper():
        try:
            result.append(func(*args, **kwargs))
        except Exception as e:
            error.append(e)
 
    thread = threading.Thread(target=wrapper)
    thread.daemon = True
    thread.start()
    thread.join(timeout)
 
    if thread.is_alive():
        print(f"警告: {func.__name__} 超时（{timeout}秒），跳过此方法")
        return None
 
    if error:
        raise error[0]
 
    return result[0]
 
def main():
    print(f"目标值: {TARGET}")
 
    # 生成波动后的系数
    FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES]
 
    # 尝试基础系数
    print(f"\n==== 尝试基础系数 ====")
 
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        base_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
        }
 
        # 显示三变量解
        if base_solutions['three'] and len(base_solutions['three']) > 0:
            display_solutions(base_solutions['three'], 3)
            print(f"\n使用基础系数列表，共找到有效解")
            return
        else:
            print("\n基础系数三变量无解，尝试波动系数")
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        base_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)),
            'three': []
        }
 
        # 检查是否有解
        has_solution = False
 
        # 显示单变量解
        if base_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1)
 
        # 显示双变量解
        if base_solutions['two'] and len(base_solutions['two']) > 0:
            has_solution = True
            display_solutions(base_solutions['two'], 2)
 
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
 
            if base_solutions['three'] and len(base_solutions['three']) > 0:
                has_solution = True
                display_solutions(base_solutions['three'], 3)
 
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用基础系数列表，共找到有效解")
            return
 
    # 如果基础系数没有找到解，尝试波动系数
    print(f"\n==== 尝试波动系数 ====")
 
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        fluctuated_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
        }
 
        # 显示三变量解
        if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
            display_solutions(fluctuated_solutions['three'], 3)
            print(f"\n使用波动系数列表，共找到有效解")
            return
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        fluctuated_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'three': []
        }
 
        # 重置标志
        has_solution = False
 
        # 显示单变量解
        if fluctuated_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1)
 
        # 显示双变量解
        if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0:
            has_solution = True
            display_solutions(fluctuated_solutions['two'], 2)
 
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
 
            if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
                has_solution = True
                display_solutions(fluctuated_solutions['three'], 3)
 
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用波动系数列表，共找到有效解")
            return
 
    # 如果所有系数集都没有找到解
    print("\n没有找到符合条件的解，即使使用波动后的系数列表。")
 
if __name__ == "__main__":
    start_time = time.time()
    main()
    print(f"\n总耗时: {time.time() - start_time:.2f}秒")

from itertools import product, combinations_with_replacement
import time
import threading
from collections import defaultdict
import math

# 配置参数（可根据需要修改）
TARGET = 98169  # 目标值
BASE_VALUES = [36.5, 41.5, 59,68.5, 74, 91.5]  # 基础系数列表
FLUCTUATION = 1.0  # 系数波动范围
MAX_SOLUTIONS = 3  # 每个组合的最大解数量
SOLVER_TIMEOUT = 180  # 求解超时时间(秒)
THREE_VAR_THRESHOLD = 220000  # 使用三个变量的阈值
PRODUCT_RANGE_THRESHOLD = 148000  # 乘积范围限制阈值
HIGH_TARGET_THRESHOLD = 260000  # 更高目标值阈值
SHOW_PROGRESS = True  # 是否显示进度
MAX_SOLUTIONS_PER_COMB = 100  # 每个组合的最大解数量，用于提前终止

def is_valid_product(p):
    """检查单个乘积是否在有效范围内"""
    if TARGET > PRODUCT_RANGE_THRESHOLD:
        if TARGET > HIGH_TARGET_THRESHOLD:
            return p <= 115000  # 目标值超过260000时，仅限制最大值
        else:
            return 74000 <= p <= 115000  # 目标值在148000-260000之间时，使用原范围
    else:
        return True  # 目标值较小时不限制乘积范围

def find_single_variable_solutions(values):
    """查找单个数的解（a*x = TARGET）"""
    solutions = []
    for a in values:
        x = TARGET / a
        if x.is_integer() and 1 <= x <= 10000 and is_valid_product(a * x):
            solutions.append((a, x))
            if len(solutions) >= MAX_SOLUTIONS:
                return solutions  # 提前终止
    return solutions

def find_two_variable_solutions(values):
    """查找两个变量的解（a*x + b*y = TARGET）"""
    solutions = defaultdict(list)
    
    # 生成所有可能的(a, b)组合
    for a in values:
        for b in values:
            if a == b:  # 避免重复
                continue
                
            # 计算x的有效范围
            min_x = max(1, math.ceil((TARGET - b * 10000) / a))
            max_x = min(math.floor((TARGET - 1) / a), 10000)
            
            if max_x < min_x:
                continue
                
            for x in range(min_x, max_x + 1):
                remainder = TARGET - a * x
                
                # 检查remainder是否在可能的范围内
                if remainder < 1 or remainder > b * 10000:
                    continue
                    
                # 检查remainder是否能被b整除
                if remainder % b == 0:
                    y = remainder // b
                    if 1 <= y <= 10000 and is_valid_product(b * y):
                        solutions[(a, b)].append((a, x, b, y))
                        if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB:
                            break  # 提前终止当前组合的搜索
    
    return solutions

def find_three_variable_solutions(values):
    """优化的三变量求解算法"""
    solutions = defaultdict(list)
    
    # 对系数进行排序，便于剪枝
    sorted_values = sorted(values)
    
    # 预计算每个系数的有效范围
    value_ranges = {}
    for a in sorted_values:
        if TARGET > PRODUCT_RANGE_THRESHOLD:
            if TARGET > HIGH_TARGET_THRESHOLD:
                min_x = max(1, math.ceil(1 / a))  # 取消下限，最小为1
                max_x = min(10000, math.floor(115000 / a))
            else:
                min_x = max(1, math.ceil(74000 / a))
                max_x = min(10000, math.floor(115000 / a))
        else:
            min_x = 1
            max_x = 10000
        value_ranges[a] = (min_x, max_x)
    
    total_combinations = len(sorted_values) * (len(sorted_values) - 1) * (len(sorted_values) - 2) // 6
    processed_combinations = 0
    
    # 三重循环，但添加了更多剪枝条件
    for i, a in enumerate(sorted_values):
        min_x, max_x = value_ranges[a]
        
        # 计算可能的x值数量，决定步长
        x_count = max_x - min_x + 1
        x_step = max(1, x_count // 1000)  # 自适应步长
        
        for x in range(min_x, max_x + 1, x_step):
            ax = a * x
            if not is_valid_product(ax):
                continue
                
            remainder1 = TARGET - ax
            if TARGET > PRODUCT_RANGE_THRESHOLD:
                if TARGET > HIGH_TARGET_THRESHOLD:
                    if remainder1 < 0:
                        continue
                else:
                    if remainder1 < 2 * 74000:
                        continue
                
            # 限制b的选择范围，避免重复组合
            for j in range(i + 1, len(sorted_values)):
                b = sorted_values[j]
                
                if TARGET > PRODUCT_RANGE_THRESHOLD:
                    if TARGET > HIGH_TARGET_THRESHOLD:
                        min_y = max(1, math.ceil(1 / b))  # 取消下限，最小为1
                        max_y = min(10000, math.floor(remainder1 / b))
                    else:
                        min_y = max(1, math.ceil(74000 / b))
                        max_y = min(10000, math.floor((remainder1 - 74000) / b))
                else:
                    min_y = 1
                    max_y = math.floor(remainder1 / b)
                    
                if max_y < min_y:
                    continue
                    
                # 计算可能的y值数量，决定步长
                y_count = max_y - min_y + 1
                y_step = max(1, y_count // 100)  # 自适应步长
                
                for y in range(min_y, max_y + 1, y_step):
                    by = b * y
                    if not is_valid_product(by):
                        continue
                        
                    remainder2 = remainder1 - by
                    if TARGET > PRODUCT_RANGE_THRESHOLD:
                        if TARGET > HIGH_TARGET_THRESHOLD:
                            if remainder2 < 0 or remainder2 > 115000:
                                continue
                        else:
                            if remainder2 < 74000 or remainder2 > 115000:
                                continue
                        
                    # 限制c的选择范围
                    found_solution = False
                    for k in range(j + 1, len(sorted_values)):
                        c = sorted_values[k]
                        
                        # 检查remainder2是否能被c整除
                        if remainder2 % c != 0:
                            continue
                            
                        z = remainder2 // c
                        if 1 <= z <= 10000 and is_valid_product(c * z):
                            key = (a, b, c)
                            solutions[key].append((a, x, b, y, c, z))
                            found_solution = True
                            if len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                                break  # 提前终止当前组合的搜索
                    
                    # 如果找到解且达到最大数量，跳出y循环
                    if found_solution and len(solutions[key]) >= MAX_SOLUTIONS_PER_COMB:
                        break  # 跳出y循环
                            
                # 进度显示
                if SHOW_PROGRESS and j % 10 == 0:
                    print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组", end='')
                processed_combinations += 1
    
    if SHOW_PROGRESS:
        print(f"\r三变量组合进度: {processed_combinations}/{total_combinations} 组 - 完成")
    
    return solutions

def find_balanced_solutions(solutions, var_count, num=2):
    """从所有解中筛选出最平衡的解"""
    if var_count == 1 or not solutions:
        return solutions  # 单变量或无解时直接返回
    
    # 当目标值超过220000时，不计算平衡解
    if TARGET > THREE_VAR_THRESHOLD:
        return []
    
    # 计算解的平衡性（变量间差异最小）
    balanced = []
    for sol in solutions:
        vars = sol[1::2]  # 提取x, y, z
        diff = max(vars) - min(vars)
        balanced.append((diff, sol))
    
    # 按差异排序，取前num个
    return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]]

def find_original_solutions(solutions, balanced_solutions, num=3):
    """从剩余解中获取原始顺序的解"""
    if not solutions:
        return []
    
    # 排除已在平衡解中的项
    remaining = [s for s in solutions if s not in balanced_solutions]
    return remaining[:num]

def display_solutions(solutions_dict, var_count):
    """优化的解显示函数"""
    if not solutions_dict:
        return
    
    print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解：")
    
    for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1):
        # 当目标值超过220000时，不显示平衡解
        if TARGET > THREE_VAR_THRESHOLD:
            all_display = pair_solutions[:MAX_SOLUTIONS]
            print_tag = "[原始解]"
        else:
            # 计算平衡解和原始解
            balanced = find_balanced_solutions(pair_solutions, var_count)
            original = find_original_solutions(pair_solutions, balanced)
            all_display = balanced + original
        
        if var_count == 1:
            a = coeffs
            print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)")
        elif var_count == 2:
            a, b = coeffs
            print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)")
        else:  # var_count == 3
            a, b, c = coeffs
            print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)")
        
        for j, sol in enumerate(all_display, 1):
            if TARGET > THREE_VAR_THRESHOLD:
                tag = print_tag
            else:
                tag = "[平衡解]" if j <= len(balanced) else "[原始解]"
            
            if var_count == 1:
                a, x = sol
                print(f"  {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}")
            elif var_count == 2:
                a, x, b, y = sol
                print(f"  {j}. x={x}, y={y}, a*x={a*x:.1f}, b*y={b*y:.1f}, 总和={a*x + b*y:.1f} {tag}")
            else:  # var_count == 3
                a, x, b, y, c, z = sol
                print(f"  {j}. x={x}, y={y}, z={z}, "
                      f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, "
                      f"总和={a*x + b*y + c*z:.1f} {tag}")

def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT):
    """运行函数并设置超时限制"""
    if kwargs is None:
        kwargs = {}
    
    result = []
    error = []
    
    def wrapper():
        try:
            result.append(func(*args, **kwargs))
        except Exception as e:
            error.append(e)
    
    thread = threading.Thread(target=wrapper)
    thread.daemon = True
    thread.start()
    thread.join(timeout)
    
    if thread.is_alive():
        print(f"警告: {func.__name__} 超时（{timeout}秒），跳过此方法")
        return None
    
    if error:
        raise error[0]
    
    return result[0]

def main():
    print(f"目标值: {TARGET}")
    
    # 生成波动后的系数
    FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES]
    
    # 尝试基础系数
    print(f"\n==== 尝试基础系数 ====")
    
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        base_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
        }
        
        # 显示三变量解
        if base_solutions['three'] and len(base_solutions['three']) > 0:
            display_solutions(base_solutions['three'], 3)
            print(f"\n使用基础系数列表，共找到有效解")
            return
        else:
            print("\n基础系数三变量无解，尝试波动系数")
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        base_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)),
            'three': []
        }
        
        # 检查是否有解
        has_solution = False
        
        # 显示单变量解
        if base_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1)
        
        # 显示双变量解
        if base_solutions['two'] and len(base_solutions['two']) > 0:
            has_solution = True
            display_solutions(base_solutions['two'], 2)
        
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,))
            
            if base_solutions['three'] and len(base_solutions['three']) > 0:
                has_solution = True
                display_solutions(base_solutions['three'], 3)
        
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用基础系数列表，共找到有效解")
            return
    
    # 如果基础系数没有找到解，尝试波动系数
    print(f"\n==== 尝试波动系数 ====")
    
    # 检查目标值是否超过阈值
    if TARGET > THREE_VAR_THRESHOLD:
        print(f"目标值 {TARGET} 超过阈值 {THREE_VAR_THRESHOLD}，只尝试三变量解")
        fluctuated_solutions = {
            'single': [],
            'two': [],
            'three': run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
        }
        
        # 显示三变量解
        if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
            display_solutions(fluctuated_solutions['three'], 3)
            print(f"\n使用波动系数列表，共找到有效解")
            return
    else:
        # 目标值未超过阈值，按顺序尝试单、双、三变量解
        fluctuated_solutions = {
            'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)),
            'three': []
        }
        
        # 重置标志
        has_solution = False
        
        # 显示单变量解
        if fluctuated_solutions['single']:
            has_solution = True
            display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1)
        
        # 显示双变量解
        if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0:
            has_solution = True
            display_solutions(fluctuated_solutions['two'], 2)
        
        # 单变量和双变量都无解时，尝试三变量解
        if not has_solution:
            print(f"\n==== 单变量和双变量无解，尝试三变量解 ====")
            fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,))
            
            if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0:
                has_solution = True
                display_solutions(fluctuated_solutions['three'], 3)
        
        # 如果找到解，退出程序
        if has_solution:
            print(f"\n使用波动系数列表，共找到有效解")
            return
    
    # 如果所有系数集都没有找到解
    print("\n没有找到符合条件的解，即使使用波动后的系数列表。")

if __name__ == "__main__":
    start_time = time.time()
    main()
    print(f"\n总耗时: {time.time() - start_time:.2f}秒")    

Success #stdin #stdout 0.07s 10704KB

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Standard input is empty

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目标值: 98169

==== 尝试基础系数 ====

找到 30 组2变量解：

1. 组合: a=36.5, b=41.5 (33 个有效解)
  1. x=1249, y=1267.0, a*x=45588.5, b*y=52580.5, 总和=98169.0 [平衡解]
  2. x=1332, y=1194.0, a*x=48618.0, b*y=49551.0, 总和=98169.0 [平衡解]
  3. x=4, y=2362.0, a*x=146.0, b*y=98023.0, 总和=98169.0 [原始解]
  4. x=87, y=2289.0, a*x=3175.5, b*y=94993.5, 总和=98169.0 [原始解]
  5. x=170, y=2216.0, a*x=6205.0, b*y=91964.0, 总和=98169.0 [原始解]

2. 组合: a=36.5, b=59 (23 个有效解)
  1. x=1002, y=1044.0, a*x=36573.0, b*y=61596.0, 总和=98169.0 [平衡解]
  2. x=1120, y=971.0, a*x=40880.0, b*y=57289.0, 总和=98169.0 [平衡解]
  3. x=58, y=1628.0, a*x=2117.0, b*y=96052.0, 总和=98169.0 [原始解]
  4. x=176, y=1555.0, a*x=6424.0, b*y=91745.0, 总和=98169.0 [原始解]
  5. x=294, y=1482.0, a*x=10731.0, b*y=87438.0, 总和=98169.0 [原始解]

3. 组合: a=36.5, b=68.5 (20 个有效解)
  1. x=978, y=912.0, a*x=35697.0, b*y=62472.0, 总和=98169.0 [平衡解]
  2. x=841, y=985.0, a*x=30696.5, b*y=67472.5, 总和=98169.0 [平衡解]
  3. x=19, y=1423.0, a*x=693.5, b*y=97475.5, 总和=98169.0 [原始解]
  4. x=156, y=1350.0, a*x=5694.0, b*y=92475.0, 总和=98169.0 [原始解]
  5. x=293, y=1277.0, a*x=10694.5, b*y=87474.5, 总和=98169.0 [原始解]

4. 组合: a=36.5, b=74 (18 个有效解)
  1. x=946, y=860.0, a*x=34529.0, b*y=63640.0, 总和=98169.0 [平衡解]
  2. x=798, y=933.0, a*x=29127.0, b*y=69042.0, 总和=98169.0 [平衡解]
  3. x=58, y=1298.0, a*x=2117.0, b*y=96052.0, 总和=98169.0 [原始解]
  4. x=206, y=1225.0, a*x=7519.0, b*y=90650.0, 总和=98169.0 [原始解]
  5. x=354, y=1152.0, a*x=12921.0, b*y=85248.0, 总和=98169.0 [原始解]

5. 组合: a=36.5, b=91.5 (15 个有效解)
  1. x=837, y=739.0, a*x=30550.5, b*y=67618.5, 总和=98169.0 [平衡解]
  2. x=654, y=812.0, a*x=23871.0, b*y=74298.0, 总和=98169.0 [平衡解]
  3. x=105, y=1031.0, a*x=3832.5, b*y=94336.5, 总和=98169.0 [原始解]
  4. x=288, y=958.0, a*x=10512.0, b*y=87657.0, 总和=98169.0 [原始解]
  5. x=471, y=885.0, a*x=17191.5, b*y=80977.5, 总和=98169.0 [原始解]

6. 组合: a=41.5, b=36.5 (33 个有效解)
  1. x=1267, y=1249.0, a*x=52580.5, b*y=45588.5, 总和=98169.0 [平衡解]
  2. x=1194, y=1332.0, a*x=49551.0, b*y=48618.0, 总和=98169.0 [平衡解]
  3. x=26, y=2660.0, a*x=1079.0, b*y=97090.0, 总和=98169.0 [原始解]
  4. x=99, y=2577.0, a*x=4108.5, b*y=94060.5, 总和=98169.0 [原始解]
  5. x=172, y=2494.0, a*x=7138.0, b*y=91031.0, 总和=98169.0 [原始解]

7. 组合: a=41.5, b=59 (20 个有效解)
  1. x=968, y=983.0, a*x=40172.0, b*y=57997.0, 总和=98169.0 [平衡解]
  2. x=1086, y=900.0, a*x=45069.0, b*y=53100.0, 总和=98169.0 [平衡解]
  3. x=24, y=1647.0, a*x=996.0, b*y=97173.0, 总和=98169.0 [原始解]
  4. x=142, y=1564.0, a*x=5893.0, b*y=92276.0, 总和=98169.0 [原始解]
  5. x=260, y=1481.0, a*x=10790.0, b*y=87379.0, 总和=98169.0 [原始解]

8. 组合: a=41.5, b=68.5 (17 个有效解)
  1. x=946, y=860.0, a*x=39259.0, b*y=58910.0, 总和=98169.0 [平衡解]
  2. x=809, y=943.0, a*x=33573.5, b*y=64595.5, 总和=98169.0 [平衡解]
  3. x=124, y=1358.0, a*x=5146.0, b*y=93023.0, 总和=98169.0 [原始解]
  4. x=261, y=1275.0, a*x=10831.5, b*y=87337.5, 总和=98169.0 [原始解]
  5. x=398, y=1192.0, a*x=16517.0, b*y=81652.0, 总和=98169.0 [原始解]

9. 组合: a=41.5, b=74 (16 个有效解)
  1. x=898, y=823.0, a*x=37267.0, b*y=60902.0, 总和=98169.0 [平衡解]
  2. x=750, y=906.0, a*x=31125.0, b*y=67044.0, 总和=98169.0 [平衡解]
  3. x=10, y=1321.0, a*x=415.0, b*y=97754.0, 总和=98169.0 [原始解]
  4. x=158, y=1238.0, a*x=6557.0, b*y=91612.0, 总和=98169.0 [原始解]
  5. x=306, y=1155.0, a*x=12699.0, b*y=85470.0, 总和=98169.0 [原始解]

10. 组合: a=41.5, b=91.5 (13 个有效解)
  1. x=756, y=730.0, a*x=31374.0, b*y=66795.0, 总和=98169.0 [平衡解]
  2. x=573, y=813.0, a*x=23779.5, b*y=74389.5, 总和=98169.0 [平衡解]
  3. x=24, y=1062.0, a*x=996.0, b*y=97173.0, 总和=98169.0 [原始解]
  4. x=207, y=979.0, a*x=8590.5, b*y=89578.5, 总和=98169.0 [原始解]
  5. x=390, y=896.0, a*x=16185.0, b*y=81984.0, 总和=98169.0 [原始解]

11. 组合: a=59, b=36.5 (23 个有效解)
  1. x=1044, y=1002.0, a*x=61596.0, b*y=36573.0, 总和=98169.0 [平衡解]
  2. x=971, y=1120.0, a*x=57289.0, b*y=40880.0, 总和=98169.0 [平衡解]
  3. x=22, y=2654.0, a*x=1298.0, b*y=96871.0, 总和=98169.0 [原始解]
  4. x=95, y=2536.0, a*x=5605.0, b*y=92564.0, 总和=98169.0 [原始解]
  5. x=168, y=2418.0, a*x=9912.0, b*y=88257.0, 总和=98169.0 [原始解]

12. 组合: a=59, b=41.5 (20 个有效解)
  1. x=983, y=968.0, a*x=57997.0, b*y=40172.0, 总和=98169.0 [平衡解]
  2. x=900, y=1086.0, a*x=53100.0, b*y=45069.0, 总和=98169.0 [平衡解]
  3. x=70, y=2266.0, a*x=4130.0, b*y=94039.0, 总和=98169.0 [原始解]
  4. x=153, y=2148.0, a*x=9027.0, b*y=89142.0, 总和=98169.0 [原始解]
  5. x=236, y=2030.0, a*x=13924.0, b*y=84245.0, 总和=98169.0 [原始解]

13. 组合: a=59, b=68.5 (12 个有效解)
  1. x=749, y=788.0, a*x=44191.0, b*y=53978.0, 总和=98169.0 [平衡解]
  2. x=886, y=670.0, a*x=52274.0, b*y=45895.0, 总和=98169.0 [平衡解]
  3. x=64, y=1378.0, a*x=3776.0, b*y=94393.0, 总和=98169.0 [原始解]
  4. x=201, y=1260.0, a*x=11859.0, b*y=86310.0, 总和=98169.0 [原始解]
  5. x=338, y=1142.0, a*x=19942.0, b*y=78227.0, 总和=98169.0 [原始解]

14. 组合: a=59, b=74 (22 个有效解)
  1. x=737, y=739, a*x=43483.0, b*y=54686.0, 总和=98169.0 [平衡解]
  2. x=811, y=680, a*x=47849.0, b*y=50320.0, 总和=98169.0 [平衡解]
  3. x=71, y=1270, a*x=4189.0, b*y=93980.0, 总和=98169.0 [原始解]
  4. x=145, y=1211, a*x=8555.0, b*y=89614.0, 总和=98169.0 [原始解]
  5. x=219, y=1152, a*x=12921.0, b*y=85248.0, 总和=98169.0 [原始解]

15. 组合: a=59, b=91.5 (9 个有效解)
  1. x=600, y=686.0, a*x=35400.0, b*y=62769.0, 总和=98169.0 [平衡解]
  2. x=783, y=568.0, a*x=46197.0, b*y=51972.0, 总和=98169.0 [平衡解]
  3. x=51, y=1040.0, a*x=3009.0, b*y=95160.0, 总和=98169.0 [原始解]
  4. x=234, y=922.0, a*x=13806.0, b*y=84363.0, 总和=98169.0 [原始解]
  5. x=417, y=804.0, a*x=24603.0, b*y=73566.0, 总和=98169.0 [原始解]

16. 组合: a=68.5, b=36.5 (20 个有效解)
  1. x=912, y=978.0, a*x=62472.0, b*y=35697.0, 总和=98169.0 [平衡解]
  2. x=985, y=841.0, a*x=67472.5, b*y=30696.5, 总和=98169.0 [平衡解]
  3. x=36, y=2622.0, a*x=2466.0, b*y=95703.0, 总和=98169.0 [原始解]
  4. x=109, y=2485.0, a*x=7466.5, b*y=90702.5, 总和=98169.0 [原始解]
  5. x=182, y=2348.0, a*x=12467.0, b*y=85702.0, 总和=98169.0 [原始解]

17. 组合: a=68.5, b=41.5 (17 个有效解)
  1. x=860, y=946.0, a*x=58910.0, b*y=39259.0, 总和=98169.0 [平衡解]
  2. x=943, y=809.0, a*x=64595.5, b*y=33573.5, 总和=98169.0 [平衡解]
  3. x=30, y=2316.0, a*x=2055.0, b*y=96114.0, 总和=98169.0 [原始解]
  4. x=113, y=2179.0, a*x=7740.5, b*y=90428.5, 总和=98169.0 [原始解]
  5. x=196, y=2042.0, a*x=13426.0, b*y=84743.0, 总和=98169.0 [原始解]

18. 组合: a=68.5, b=59 (12 个有效解)
  1. x=788, y=749.0, a*x=53978.0, b*y=44191.0, 总和=98169.0 [平衡解]
  2. x=670, y=886.0, a*x=45895.0, b*y=52274.0, 总和=98169.0 [平衡解]
  3. x=80, y=1571.0, a*x=5480.0, b*y=92689.0, 总和=98169.0 [原始解]
  4. x=198, y=1434.0, a*x=13563.0, b*y=84606.0, 总和=98169.0 [原始解]
  5. x=316, y=1297.0, a*x=21646.0, b*y=76523.0, 总和=98169.0 [原始解]

19. 组合: a=68.5, b=74 (10 个有效解)
  1. x=678, y=699.0, a*x=46443.0, b*y=51726.0, 总和=98169.0 [平衡解]
  2. x=826, y=562.0, a*x=56581.0, b*y=41588.0, 总和=98169.0 [平衡解]
  3. x=86, y=1247.0, a*x=5891.0, b*y=92278.0, 总和=98169.0 [原始解]
  4. x=234, y=1110.0, a*x=16029.0, b*y=82140.0, 总和=98169.0 [原始解]
  5. x=382, y=973.0, a*x=26167.0, b*y=72002.0, 总和=98169.0 [原始解]

20. 组合: a=68.5, b=91.5 (8 个有效解)
  1. x=633, y=599.0, a*x=43360.5, b*y=54808.5, 总和=98169.0 [平衡解]
  2. x=450, y=736.0, a*x=30825.0, b*y=67344.0, 总和=98169.0 [平衡解]
  3. x=84, y=1010.0, a*x=5754.0, b*y=92415.0, 总和=98169.0 [原始解]
  4. x=267, y=873.0, a*x=18289.5, b*y=79879.5, 总和=98169.0 [原始解]
  5. x=816, y=462.0, a*x=55896.0, b*y=42273.0, 总和=98169.0 [原始解]

21. 组合: a=74, b=36.5 (18 个有效解)
  1. x=860, y=946.0, a*x=63640.0, b*y=34529.0, 总和=98169.0 [平衡解]
  2. x=933, y=798.0, a*x=69042.0, b*y=29127.0, 总和=98169.0 [平衡解]
  3. x=57, y=2574.0, a*x=4218.0, b*y=93951.0, 总和=98169.0 [原始解]
  4. x=130, y=2426.0, a*x=9620.0, b*y=88549.0, 总和=98169.0 [原始解]
  5. x=203, y=2278.0, a*x=15022.0, b*y=83147.0, 总和=98169.0 [原始解]

22. 组合: a=74, b=41.5 (16 个有效解)
  1. x=823, y=898.0, a*x=60902.0, b*y=37267.0, 总和=98169.0 [平衡解]
  2. x=906, y=750.0, a*x=67044.0, b*y=31125.0, 总和=98169.0 [平衡解]
  3. x=76, y=2230.0, a*x=5624.0, b*y=92545.0, 总和=98169.0 [原始解]
  4. x=159, y=2082.0, a*x=11766.0, b*y=86403.0, 总和=98169.0 [原始解]
  5. x=242, y=1934.0, a*x=17908.0, b*y=80261.0, 总和=98169.0 [原始解]

23. 组合: a=74, b=59 (22 个有效解)
  1. x=739, y=737, a*x=54686.0, b*y=43483.0, 总和=98169.0 [平衡解]
  2. x=680, y=811, a*x=50320.0, b*y=47849.0, 总和=98169.0 [平衡解]
  3. x=31, y=1625, a*x=2294.0, b*y=95875.0, 总和=98169.0 [原始解]
  4. x=90, y=1551, a*x=6660.0, b*y=91509.0, 总和=98169.0 [原始解]
  5. x=149, y=1477, a*x=11026.0, b*y=87143.0, 总和=98169.0 [原始解]

24. 组合: a=74, b=68.5 (10 个有效解)
  1. x=699, y=678.0, a*x=51726.0, b*y=46443.0, 总和=98169.0 [平衡解]
  2. x=562, y=826.0, a*x=41588.0, b*y=56581.0, 总和=98169.0 [平衡解]
  3. x=14, y=1418.0, a*x=1036.0, b*y=97133.0, 总和=98169.0 [原始解]
  4. x=151, y=1270.0, a*x=11174.0, b*y=86995.0, 总和=98169.0 [原始解]
  5. x=288, y=1122.0, a*x=21312.0, b*y=76857.0, 总和=98169.0 [原始解]

25. 组合: a=74, b=91.5 (7 个有效解)
  1. x=513, y=658.0, a*x=37962.0, b*y=60207.0, 总和=98169.0 [平衡解]
  2. x=696, y=510.0, a*x=51504.0, b*y=46665.0, 总和=98169.0 [平衡解]
  3. x=147, y=954.0, a*x=10878.0, b*y=87291.0, 总和=98169.0 [原始解]
  4. x=330, y=806.0, a*x=24420.0, b*y=73749.0, 总和=98169.0 [原始解]
  5. x=879, y=362.0, a*x=65046.0, b*y=33123.0, 总和=98169.0 [原始解]

26. 组合: a=91.5, b=36.5 (15 个有效解)
  1. x=739, y=837.0, a*x=67618.5, b*y=30550.5, 总和=98169.0 [平衡解]
  2. x=812, y=654.0, a*x=74298.0, b*y=23871.0, 总和=98169.0 [平衡解]
  3. x=9, y=2667.0, a*x=823.5, b*y=97345.5, 总和=98169.0 [原始解]
  4. x=82, y=2484.0, a*x=7503.0, b*y=90666.0, 总和=98169.0 [原始解]
  5. x=155, y=2301.0, a*x=14182.5, b*y=83986.5, 总和=98169.0 [原始解]

27. 组合: a=91.5, b=41.5 (13 个有效解)
  1. x=730, y=756.0, a*x=66795.0, b*y=31374.0, 总和=98169.0 [平衡解]
  2. x=813, y=573.0, a*x=74389.5, b*y=23779.5, 总和=98169.0 [平衡解]
  3. x=66, y=2220.0, a*x=6039.0, b*y=92130.0, 总和=98169.0 [原始解]
  4. x=149, y=2037.0, a*x=13633.5, b*y=84535.5, 总和=98169.0 [原始解]
  5. x=232, y=1854.0, a*x=21228.0, b*y=76941.0, 总和=98169.0 [原始解]

28. 组合: a=91.5, b=59 (9 个有效解)
  1. x=686, y=600.0, a*x=62769.0, b*y=35400.0, 总和=98169.0 [平衡解]
  2. x=568, y=783.0, a*x=51972.0, b*y=46197.0, 总和=98169.0 [平衡解]
  3. x=96, y=1515.0, a*x=8784.0, b*y=89385.0, 总和=98169.0 [原始解]
  4. x=214, y=1332.0, a*x=19581.0, b*y=78588.0, 总和=98169.0 [原始解]
  5. x=332, y=1149.0, a*x=30378.0, b*y=67791.0, 总和=98169.0 [原始解]

29. 组合: a=91.5, b=68.5 (8 个有效解)
  1. x=599, y=633.0, a*x=54808.5, b*y=43360.5, 总和=98169.0 [平衡解]
  2. x=736, y=450.0, a*x=67344.0, b*y=30825.0, 总和=98169.0 [平衡解]
  3. x=51, y=1365.0, a*x=4666.5, b*y=93502.5, 总和=98169.0 [原始解]
  4. x=188, y=1182.0, a*x=17202.0, b*y=80967.0, 总和=98169.0 [原始解]
  5. x=325, y=999.0, a*x=29737.5, b*y=68431.5, 总和=98169.0 [原始解]

30. 组合: a=91.5, b=74 (7 个有效解)
  1. x=658, y=513.0, a*x=60207.0, b*y=37962.0, 总和=98169.0 [平衡解]
  2. x=510, y=696.0, a*x=46665.0, b*y=51504.0, 总和=98169.0 [平衡解]
  3. x=66, y=1245.0, a*x=6039.0, b*y=92130.0, 总和=98169.0 [原始解]
  4. x=214, y=1062.0, a*x=19581.0, b*y=78588.0, 总和=98169.0 [原始解]
  5. x=362, y=879.0, a*x=33123.0, b*y=65046.0, 总和=98169.0 [原始解]

使用基础系数列表，共找到有效解

总耗时: 0.03秒

https://ideone.com/Lv0G1U

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Python 3 nbc (python 3.7.3)

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