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from itertools import product
 
# 定义目标数字（可根据需要修改）
TARGET = 132001
 
def find_solutions():
    a_values =  [35, 40.5, 58, 67, 73, 90.5]
    solutions_by_pair = {}
 
    total_iterations = len(a_values) ** 2 * 10000
    print(f"总计算次数: {total_iterations:,}")
 
    count = 0
    for a, b in product(a_values, repeat=2):
        min_x = 1
        max_x = int((TARGET - 1) // a)
 
        if max_x < min_x:
            continue
 
        all_solutions = []  # 存储所有解
        for x in range(min_x, max_x + 1):
            numerator = TARGET - a * x
            if numerator <= 0:
                continue
 
            y = numerator / b
            if y.is_integer() and 1 <= y <= 10000:
                all_solutions.append((x, int(y)))
 
            count += 1
            if count % 1000000 == 0:
                progress = count / total_iterations * 100
                print(f"进度: {progress:.2f}%")
 
        if all_solutions:
            # 按平衡度排序，取前2个平衡解
            balanced_solutions = sorted(all_solutions, key=lambda p: abs(p[0] - p[1]))[:2]
 
            # 从原始解中排除已在平衡解中的项，取前3个
            remaining_solutions = [s for s in all_solutions if s not in balanced_solutions][:3]
 
            # 合并：先2个平衡解，再3个原始解
            combined = balanced_solutions + remaining_solutions
 
            solutions_by_pair[(a, b)] = combined
 
    return solutions_by_pair
 
def display_solutions(solutions_by_pair):
    total_pairs = len(solutions_by_pair)
    print(f"共找到 {total_pairs} 组有效(a, b)组合，目标值为 {TARGET}")
 
    if total_pairs == 0:
        return
 
    sorted_pairs = sorted(solutions_by_pair.keys(), key=lambda x: (x[0], x[1]))
 
    for i, (a, b) in enumerate(sorted_pairs, 1):
        solutions = solutions_by_pair[(a, b)]
        print(f"\n{i}. 组合 a={a}, b={b}: {len(solutions)} 个解")
 
        for j, (x, y) in enumerate(solutions, 1):
            diff = abs(x - y)
            ax = a * x
            by = b * y
            tag = "[平衡解]" if j <= 2 else "[原始解]"
            print(f"   {j}. x={x}, y={y}  (差值: {diff}, a*x={ax}, b*y={by}, a*x + b*y = {ax + by:.1f}) {tag}")
 
if __name__ == "__main__":
    import time
    start_time = time.time()
 
    solutions_by_pair = find_solutions()
    display_solutions(solutions_by_pair)
 
    print(f"计算耗时: {time.time() - start_time:.2f}秒")

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Success #stdin #stdout 0.07s 9676KB

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Standard input is empty

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总计算次数: 360,000
共找到 30 组有效(a, b)组合，目标值为 132001

1. 组合 a=35, b=40.5: 5 个解
   1. x=1721, y=1772  (差值: 51, a*x=60235, b*y=71766.0, a*x + b*y = 132001.0) [平衡解]
   2. x=1802, y=1702  (差值: 100, a*x=63070, b*y=68931.0, a*x + b*y = 132001.0) [平衡解]
   3. x=20, y=3242  (差值: 3222, a*x=700, b*y=131301.0, a*x + b*y = 132001.0) [原始解]
   4. x=101, y=3172  (差值: 3071, a*x=3535, b*y=128466.0, a*x + b*y = 132001.0) [原始解]
   5. x=182, y=3102  (差值: 2920, a*x=6370, b*y=125631.0, a*x + b*y = 132001.0) [原始解]

2. 组合 a=35, b=58: 5 个解
   1. x=1415, y=1422  (差值: 7, a*x=49525, b*y=82476, a*x + b*y = 132001.0) [平衡解]
   2. x=1473, y=1387  (差值: 86, a*x=51555, b*y=80446, a*x + b*y = 132001.0) [平衡解]
   3. x=23, y=2262  (差值: 2239, a*x=805, b*y=131196, a*x + b*y = 132001.0) [原始解]
   4. x=81, y=2227  (差值: 2146, a*x=2835, b*y=129166, a*x + b*y = 132001.0) [原始解]
   5. x=139, y=2192  (差值: 2053, a*x=4865, b*y=127136, a*x + b*y = 132001.0) [原始解]

3. 组合 a=35, b=67: 5 个解
   1. x=1325, y=1278  (差值: 47, a*x=46375, b*y=85626, a*x + b*y = 132001.0) [平衡解]
   2. x=1258, y=1313  (差值: 55, a*x=44030, b*y=87971, a*x + b*y = 132001.0) [平衡解]
   3. x=52, y=1943  (差值: 1891, a*x=1820, b*y=130181, a*x + b*y = 132001.0) [原始解]
   4. x=119, y=1908  (差值: 1789, a*x=4165, b*y=127836, a*x + b*y = 132001.0) [原始解]
   5. x=186, y=1873  (差值: 1687, a*x=6510, b*y=125491, a*x + b*y = 132001.0) [原始解]

4. 组合 a=35, b=73: 5 个解
   1. x=1254, y=1207  (差值: 47, a*x=43890, b*y=88111, a*x + b*y = 132001.0) [平衡解]
   2. x=1181, y=1242  (差值: 61, a*x=41335, b*y=90666, a*x + b*y = 132001.0) [平衡解]
   3. x=13, y=1802  (差值: 1789, a*x=455, b*y=131546, a*x + b*y = 132001.0) [原始解]
   4. x=86, y=1767  (差值: 1681, a*x=3010, b*y=128991, a*x + b*y = 132001.0) [原始解]
   5. x=159, y=1732  (差值: 1573, a*x=5565, b*y=126436, a*x + b*y = 132001.0) [原始解]

5. 组合 a=35, b=90.5: 5 个解
   1. x=1103, y=1032  (差值: 71, a*x=38605, b*y=93396.0, a*x + b*y = 132001.0) [平衡解]
   2. x=922, y=1102  (差值: 180, a*x=32270, b*y=99731.0, a*x + b*y = 132001.0) [平衡解]
   3. x=17, y=1452  (差值: 1435, a*x=595, b*y=131406.0, a*x + b*y = 132001.0) [原始解]
   4. x=198, y=1382  (差值: 1184, a*x=6930, b*y=125071.0, a*x + b*y = 132001.0) [原始解]
   5. x=379, y=1312  (差值: 933, a*x=13265, b*y=118736.0, a*x + b*y = 132001.0) [原始解]

6. 组合 a=40.5, b=35: 5 个解
   1. x=1772, y=1721  (差值: 51, a*x=71766.0, b*y=60235, a*x + b*y = 132001.0) [平衡解]
   2. x=1702, y=1802  (差值: 100, a*x=68931.0, b*y=63070, a*x + b*y = 132001.0) [平衡解]
   3. x=22, y=3746  (差值: 3724, a*x=891.0, b*y=131110, a*x + b*y = 132001.0) [原始解]
   4. x=92, y=3665  (差值: 3573, a*x=3726.0, b*y=128275, a*x + b*y = 132001.0) [原始解]
   5. x=162, y=3584  (差值: 3422, a*x=6561.0, b*y=125440, a*x + b*y = 132001.0) [原始解]

7. 组合 a=40.5, b=58: 5 个解
   1. x=1346, y=1336  (差值: 10, a*x=54513.0, b*y=77488, a*x + b*y = 132001.0) [平衡解]
   2. x=1230, y=1417  (差值: 187, a*x=49815.0, b*y=82186, a*x + b*y = 132001.0) [平衡解]
   3. x=70, y=2227  (差值: 2157, a*x=2835.0, b*y=129166, a*x + b*y = 132001.0) [原始解]
   4. x=186, y=2146  (差值: 1960, a*x=7533.0, b*y=124468, a*x + b*y = 132001.0) [原始解]
   5. x=302, y=2065  (差值: 1763, a*x=12231.0, b*y=119770, a*x + b*y = 132001.0) [原始解]

8. 组合 a=40.5, b=67: 5 个解
   1. x=1198, y=1246  (差值: 48, a*x=48519.0, b*y=83482, a*x + b*y = 132001.0) [平衡解]
   2. x=1332, y=1165  (差值: 167, a*x=53946.0, b*y=78055, a*x + b*y = 132001.0) [平衡解]
   3. x=126, y=1894  (差值: 1768, a*x=5103.0, b*y=126898, a*x + b*y = 132001.0) [原始解]
   4. x=260, y=1813  (差值: 1553, a*x=10530.0, b*y=121471, a*x + b*y = 132001.0) [原始解]
   5. x=394, y=1732  (差值: 1338, a*x=15957.0, b*y=116044, a*x + b*y = 132001.0) [原始解]

9. 组合 a=40.5, b=73: 5 个解
   1. x=1154, y=1168  (差值: 14, a*x=46737.0, b*y=85264, a*x + b*y = 132001.0) [平衡解]
   2. x=1300, y=1087  (差值: 213, a*x=52650.0, b*y=79351, a*x + b*y = 132001.0) [平衡解]
   3. x=132, y=1735  (差值: 1603, a*x=5346.0, b*y=126655, a*x + b*y = 132001.0) [原始解]
   4. x=278, y=1654  (差值: 1376, a*x=11259.0, b*y=120742, a*x + b*y = 132001.0) [原始解]
   5. x=424, y=1573  (差值: 1149, a*x=17172.0, b*y=114829, a*x + b*y = 132001.0) [原始解]

10. 组合 a=40.5, b=90.5: 5 个解
   1. x=1056, y=986  (差值: 70, a*x=42768.0, b*y=89233.0, a*x + b*y = 132001.0) [平衡解]
   2. x=875, y=1067  (差值: 192, a*x=35437.5, b*y=96563.5, a*x + b*y = 132001.0) [平衡解]
   3. x=151, y=1391  (差值: 1240, a*x=6115.5, b*y=125885.5, a*x + b*y = 132001.0) [原始解]
   4. x=332, y=1310  (差值: 978, a*x=13446.0, b*y=118555.0, a*x + b*y = 132001.0) [原始解]
   5. x=513, y=1229  (差值: 716, a*x=20776.5, b*y=111224.5, a*x + b*y = 132001.0) [原始解]

11. 组合 a=58, b=35: 5 个解
   1. x=1422, y=1415  (差值: 7, a*x=82476, b*y=49525, a*x + b*y = 132001.0) [平衡解]
   2. x=1387, y=1473  (差值: 86, a*x=80446, b*y=51555, a*x + b*y = 132001.0) [平衡解]
   3. x=22, y=3735  (差值: 3713, a*x=1276, b*y=130725, a*x + b*y = 132001.0) [原始解]
   4. x=57, y=3677  (差值: 3620, a*x=3306, b*y=128695, a*x + b*y = 132001.0) [原始解]
   5. x=92, y=3619  (差值: 3527, a*x=5336, b*y=126665, a*x + b*y = 132001.0) [原始解]

12. 组合 a=58, b=40.5: 5 个解
   1. x=1336, y=1346  (差值: 10, a*x=77488, b*y=54513.0, a*x + b*y = 132001.0) [平衡解]
   2. x=1417, y=1230  (差值: 187, a*x=82186, b*y=49815.0, a*x + b*y = 132001.0) [平衡解]
   3. x=40, y=3202  (差值: 3162, a*x=2320, b*y=129681.0, a*x + b*y = 132001.0) [原始解]
   4. x=121, y=3086  (差值: 2965, a*x=7018, b*y=124983.0, a*x + b*y = 132001.0) [原始解]
   5. x=202, y=2970  (差值: 2768, a*x=11716, b*y=120285.0, a*x + b*y = 132001.0) [原始解]

13. 组合 a=58, b=67: 5 个解
   1. x=1041, y=1069  (差值: 28, a*x=60378, b*y=71623, a*x + b*y = 132001.0) [平衡解]
   2. x=1108, y=1011  (差值: 97, a*x=64264, b*y=67737, a*x + b*y = 132001.0) [平衡解]
   3. x=36, y=1939  (差值: 1903, a*x=2088, b*y=129913, a*x + b*y = 132001.0) [原始解]
   4. x=103, y=1881  (差值: 1778, a*x=5974, b*y=126027, a*x + b*y = 132001.0) [原始解]
   5. x=170, y=1823  (差值: 1653, a*x=9860, b*y=122141, a*x + b*y = 132001.0) [原始解]

14. 组合 a=58, b=73: 5 个解
   1. x=1016, y=1001  (差值: 15, a*x=58928, b*y=73073, a*x + b*y = 132001.0) [平衡解]
   2. x=943, y=1059  (差值: 116, a*x=54694, b*y=77307, a*x + b*y = 132001.0) [平衡解]
   3. x=67, y=1755  (差值: 1688, a*x=3886, b*y=128115, a*x + b*y = 132001.0) [原始解]
   4. x=140, y=1697  (差值: 1557, a*x=8120, b*y=123881, a*x + b*y = 132001.0) [原始解]
   5. x=213, y=1639  (差值: 1426, a*x=12354, b*y=119647, a*x + b*y = 132001.0) [原始解]

15. 组合 a=58, b=90.5: 5 个解
   1. x=831, y=926  (差值: 95, a*x=48198, b*y=83803.0, a*x + b*y = 132001.0) [平衡解]
   2. x=1012, y=810  (差值: 202, a*x=58696, b*y=73305.0, a*x + b*y = 132001.0) [平衡解]
   3. x=107, y=1390  (差值: 1283, a*x=6206, b*y=125795.0, a*x + b*y = 132001.0) [原始解]
   4. x=288, y=1274  (差值: 986, a*x=16704, b*y=115297.0, a*x + b*y = 132001.0) [原始解]
   5. x=469, y=1158  (差值: 689, a*x=27202, b*y=104799.0, a*x + b*y = 132001.0) [原始解]

16. 组合 a=67, b=35: 5 个解
   1. x=1278, y=1325  (差值: 47, a*x=85626, b*y=46375, a*x + b*y = 132001.0) [平衡解]
   2. x=1313, y=1258  (差值: 55, a*x=87971, b*y=44030, a*x + b*y = 132001.0) [平衡解]
   3. x=18, y=3737  (差值: 3719, a*x=1206, b*y=130795, a*x + b*y = 132001.0) [原始解]
   4. x=53, y=3670  (差值: 3617, a*x=3551, b*y=128450, a*x + b*y = 132001.0) [原始解]
   5. x=88, y=3603  (差值: 3515, a*x=5896, b*y=126105, a*x + b*y = 132001.0) [原始解]

17. 组合 a=67, b=40.5: 5 个解
   1. x=1246, y=1198  (差值: 48, a*x=83482, b*y=48519.0, a*x + b*y = 132001.0) [平衡解]
   2. x=1165, y=1332  (差值: 167, a*x=78055, b*y=53946.0, a*x + b*y = 132001.0) [平衡解]
   3. x=31, y=3208  (差值: 3177, a*x=2077, b*y=129924.0, a*x + b*y = 132001.0) [原始解]
   4. x=112, y=3074  (差值: 2962, a*x=7504, b*y=124497.0, a*x + b*y = 132001.0) [原始解]
   5. x=193, y=2940  (差值: 2747, a*x=12931, b*y=119070.0, a*x + b*y = 132001.0) [原始解]

18. 组合 a=67, b=58: 5 个解
   1. x=1069, y=1041  (差值: 28, a*x=71623, b*y=60378, a*x + b*y = 132001.0) [平衡解]
   2. x=1011, y=1108  (差值: 97, a*x=67737, b*y=64264, a*x + b*y = 132001.0) [平衡解]
   3. x=25, y=2247  (差值: 2222, a*x=1675, b*y=130326, a*x + b*y = 132001.0) [原始解]
   4. x=83, y=2180  (差值: 2097, a*x=5561, b*y=126440, a*x + b*y = 132001.0) [原始解]
   5. x=141, y=2113  (差值: 1972, a*x=9447, b*y=122554, a*x + b*y = 132001.0) [原始解]

19. 组合 a=67, b=73: 5 个解
   1. x=934, y=951  (差值: 17, a*x=62578, b*y=69423, a*x + b*y = 132001.0) [平衡解]
   2. x=1007, y=884  (差值: 123, a*x=67469, b*y=64532, a*x + b*y = 132001.0) [平衡解]
   3. x=58, y=1755  (差值: 1697, a*x=3886, b*y=128115, a*x + b*y = 132001.0) [原始解]
   4. x=131, y=1688  (差值: 1557, a*x=8777, b*y=123224, a*x + b*y = 132001.0) [原始解]
   5. x=204, y=1621  (差值: 1417, a*x=13668, b*y=118333, a*x + b*y = 132001.0) [原始解]

20. 组合 a=67, b=90.5: 5 个解
   1. x=768, y=890  (差值: 122, a*x=51456, b*y=80545.0, a*x + b*y = 132001.0) [平衡解]
   2. x=949, y=756  (差值: 193, a*x=63583, b*y=68418.0, a*x + b*y = 132001.0) [平衡解]
   3. x=44, y=1426  (差值: 1382, a*x=2948, b*y=129053.0, a*x + b*y = 132001.0) [原始解]
   4. x=225, y=1292  (差值: 1067, a*x=15075, b*y=116926.0, a*x + b*y = 132001.0) [原始解]
   5. x=406, y=1158  (差值: 752, a*x=27202, b*y=104799.0, a*x + b*y = 132001.0) [原始解]

21. 组合 a=73, b=35: 5 个解
   1. x=1207, y=1254  (差值: 47, a*x=88111, b*y=43890, a*x + b*y = 132001.0) [平衡解]
   2. x=1242, y=1181  (差值: 61, a*x=90666, b*y=41335, a*x + b*y = 132001.0) [平衡解]
   3. x=17, y=3736  (差值: 3719, a*x=1241, b*y=130760, a*x + b*y = 132001.0) [原始解]
   4. x=52, y=3663  (差值: 3611, a*x=3796, b*y=128205, a*x + b*y = 132001.0) [原始解]
   5. x=87, y=3590  (差值: 3503, a*x=6351, b*y=125650, a*x + b*y = 132001.0) [原始解]

22. 组合 a=73, b=40.5: 5 个解
   1. x=1168, y=1154  (差值: 14, a*x=85264, b*y=46737.0, a*x + b*y = 132001.0) [平衡解]
   2. x=1087, y=1300  (差值: 213, a*x=79351, b*y=52650.0, a*x + b*y = 132001.0) [平衡解]
   3. x=34, y=3198  (差值: 3164, a*x=2482, b*y=129519.0, a*x + b*y = 132001.0) [原始解]
   4. x=115, y=3052  (差值: 2937, a*x=8395, b*y=123606.0, a*x + b*y = 132001.0) [原始解]
   5. x=196, y=2906  (差值: 2710, a*x=14308, b*y=117693.0, a*x + b*y = 132001.0) [原始解]

23. 组合 a=73, b=58: 5 个解
   1. x=1001, y=1016  (差值: 15, a*x=73073, b*y=58928, a*x + b*y = 132001.0) [平衡解]
   2. x=1059, y=943  (差值: 116, a*x=77307, b*y=54694, a*x + b*y = 132001.0) [平衡解]
   3. x=15, y=2257  (差值: 2242, a*x=1095, b*y=130906, a*x + b*y = 132001.0) [原始解]
   4. x=73, y=2184  (差值: 2111, a*x=5329, b*y=126672, a*x + b*y = 132001.0) [原始解]
   5. x=131, y=2111  (差值: 1980, a*x=9563, b*y=122438, a*x + b*y = 132001.0) [原始解]

24. 组合 a=73, b=67: 5 个解
   1. x=951, y=934  (差值: 17, a*x=69423, b*y=62578, a*x + b*y = 132001.0) [平衡解]
   2. x=884, y=1007  (差值: 123, a*x=64532, b*y=67469, a*x + b*y = 132001.0) [平衡解]
   3. x=13, y=1956  (差值: 1943, a*x=949, b*y=131052, a*x + b*y = 132001.0) [原始解]
   4. x=80, y=1883  (差值: 1803, a*x=5840, b*y=126161, a*x + b*y = 132001.0) [原始解]
   5. x=147, y=1810  (差值: 1663, a*x=10731, b*y=121270, a*x + b*y = 132001.0) [原始解]

25. 组合 a=73, b=90.5: 5 个解
   1. x=871, y=756  (差值: 115, a*x=63583, b*y=68418.0, a*x + b*y = 132001.0) [平衡解]
   2. x=690, y=902  (差值: 212, a*x=50370, b*y=81631.0, a*x + b*y = 132001.0) [平衡解]
   3. x=147, y=1340  (差值: 1193, a*x=10731, b*y=121270.0, a*x + b*y = 132001.0) [原始解]
   4. x=328, y=1194  (差值: 866, a*x=23944, b*y=108057.0, a*x + b*y = 132001.0) [原始解]
   5. x=509, y=1048  (差值: 539, a*x=37157, b*y=94844.0, a*x + b*y = 132001.0) [原始解]

26. 组合 a=90.5, b=35: 5 个解
   1. x=1032, y=1103  (差值: 71, a*x=93396.0, b*y=38605, a*x + b*y = 132001.0) [平衡解]
   2. x=1102, y=922  (差值: 180, a*x=99731.0, b*y=32270, a*x + b*y = 132001.0) [平衡解]
   3. x=52, y=3637  (差值: 3585, a*x=4706.0, b*y=127295, a*x + b*y = 132001.0) [原始解]
   4. x=122, y=3456  (差值: 3334, a*x=11041.0, b*y=120960, a*x + b*y = 132001.0) [原始解]
   5. x=192, y=3275  (差值: 3083, a*x=17376.0, b*y=114625, a*x + b*y = 132001.0) [原始解]

27. 组合 a=90.5, b=40.5: 5 个解
   1. x=986, y=1056  (差值: 70, a*x=89233.0, b*y=42768.0, a*x + b*y = 132001.0) [平衡解]
   2. x=1067, y=875  (差值: 192, a*x=96563.5, b*y=35437.5, a*x + b*y = 132001.0) [平衡解]
   3. x=14, y=3228  (差值: 3214, a*x=1267.0, b*y=130734.0, a*x + b*y = 132001.0) [原始解]
   4. x=95, y=3047  (差值: 2952, a*x=8597.5, b*y=123403.5, a*x + b*y = 132001.0) [原始解]
   5. x=176, y=2866  (差值: 2690, a*x=15928.0, b*y=116073.0, a*x + b*y = 132001.0) [原始解]

28. 组合 a=90.5, b=58: 5 个解
   1. x=926, y=831  (差值: 95, a*x=83803.0, b*y=48198, a*x + b*y = 132001.0) [平衡解]
   2. x=810, y=1012  (差值: 202, a*x=73305.0, b*y=58696, a*x + b*y = 132001.0) [平衡解]
   3. x=114, y=2098  (差值: 1984, a*x=10317.0, b*y=121684, a*x + b*y = 132001.0) [原始解]
   4. x=230, y=1917  (差值: 1687, a*x=20815.0, b*y=111186, a*x + b*y = 132001.0) [原始解]
   5. x=346, y=1736  (差值: 1390, a*x=31313.0, b*y=100688, a*x + b*y = 132001.0) [原始解]

29. 组合 a=90.5, b=67: 5 个解
   1. x=890, y=768  (差值: 122, a*x=80545.0, b*y=51456, a*x + b*y = 132001.0) [平衡解]
   2. x=756, y=949  (差值: 193, a*x=68418.0, b*y=63583, a*x + b*y = 132001.0) [平衡解]
   3. x=86, y=1854  (差值: 1768, a*x=7783.0, b*y=124218, a*x + b*y = 132001.0) [原始解]
   4. x=220, y=1673  (差值: 1453, a*x=19910.0, b*y=112091, a*x + b*y = 132001.0) [原始解]
   5. x=354, y=1492  (差值: 1138, a*x=32037.0, b*y=99964, a*x + b*y = 132001.0) [原始解]

30. 组合 a=90.5, b=73: 5 个解
   1. x=756, y=871  (差值: 115, a*x=68418.0, b*y=63583, a*x + b*y = 132001.0) [平衡解]
   2. x=902, y=690  (差值: 212, a*x=81631.0, b*y=50370, a*x + b*y = 132001.0) [平衡解]
   3. x=26, y=1776  (差值: 1750, a*x=2353.0, b*y=129648, a*x + b*y = 132001.0) [原始解]
   4. x=172, y=1595  (差值: 1423, a*x=15566.0, b*y=116435, a*x + b*y = 132001.0) [原始解]
   5. x=318, y=1414  (差值: 1096, a*x=28779.0, b*y=103222, a*x + b*y = 132001.0) [原始解]
计算耗时: 0.04秒

https://ideone.com/OlKGR3

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Python 3 nbc (python 3.7.3)

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