{"id":1128247,"date":"2025-01-08T20:18:27","date_gmt":"2025-01-08T12:18:27","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1128247.html"},"modified":"2025-01-08T20:18:30","modified_gmt":"2025-01-08T12:18:30","slug":"python%e5%a6%82%e4%bd%95%e5%88%a4%e6%96%ad%e4%b8%80%e4%b8%aa%e6%95%b0%e6%98%af%e8%b4%a8%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1128247.html","title":{"rendered":"python\u5982\u4f55\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u8d28\u6570"},"content":{"rendered":"

\"python\u5982\u4f55\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u8d28\u6570\"<\/p>\n

Python \u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5e38\u89c1\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u8bd5\u9664\u6cd5\u3001\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5\u30016k\u00b11\u4f18\u5316\u6cd5\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u9010\u4e00\u9664\u4ee5\u5c0f\u4e8e\u5176\u5e73\u65b9\u6839\u7684\u6240\u6709\u8d28\u6570\u3001\u5229\u7528\u7b5b\u6cd5\u9884\u5148\u6807\u8bb0\u975e\u8d28\u6570\u3001\u4ee5\u53ca\u901a\u8fc76k\u00b11\u7684\u5f62\u5f0f\u51cf\u5c11\u5224\u65ad\u6b21\u6570\u6765\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u3002<\/strong> \u5176\u4e2d\uff0c\u8bd5\u9664\u6cd5<\/strong>\u662f\u6700\u7b80\u5355\u4e14\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u9002\u7528\u4e8e\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u7684\u8d28\u6570\u5224\u65ad\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u8bd5\u9664\u6cd5<\/h3>\n<\/p>\n

\u8bd5\u9664\u6cd5\u662f\u6700\u76f4\u89c2\u548c\u57fa\u7840\u7684\u65b9\u6cd5\uff0c\u901a\u8fc7\u9010\u4e00\u68c0\u67e5\u4e00\u4e2a\u6570\u80fd\u5426\u88ab\u5c0f\u4e8e\u5176\u5e73\u65b9\u6839\u7684\u6240\u6709\u6570\u6574\u9664\u6765\u5224\u65ad\u5176\u662f\u5426\u4e3a\u8d28\u6570\u3002<\/p>\n<\/p>\n

1.1 \u57fa\u672c\u539f\u7406<\/h4>\n<\/p>\n

\u4e00\u4e2a\u6570 ( n ) \u5982\u679c\u4e0d\u662f\u8d28\u6570\uff0c\u90a3\u4e48\u5b83\u4e00\u5b9a\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u4e2a\u56e0\u6570 ( a ) \u548c ( b )\uff0c\u5373 ( n = a \\times b )\u3002\u5982\u679c ( a ) \u548c ( b ) \u90fd\u5927\u4e8e ( \\sqrt{n} )\uff0c\u90a3\u4e48 ( a \\times b ) \u5c06\u5927\u4e8e ( n )\uff0c\u8fd9\u4e0e\u5047\u8bbe\u77db\u76fe\u3002\u56e0\u6b64\uff0c\u53ea\u9700\u8981\u68c0\u67e5 ( n ) \u662f\u5426\u80fd\u88ab\u5c0f\u4e8e\u7b49\u4e8e ( \\sqrt{n} ) \u7684\u6570\u6574\u9664\u5373\u53ef\u3002<\/p>\n<\/p>\n

1.2 \u5b9e\u73b0\u4ee3\u7801<\/h4>\n<\/p>\n

import math<\/p>\n
def is_prime(n):<\/p>\n
    if n <= 1:<\/p>\n
        return False<\/p>\n
    if n <= 3:<\/p>\n
        return True<\/p>\n
    if n % 2 == 0 or n % 3 == 0:<\/p>\n
        return False<\/p>\n
    i = 5<\/p>\n
    while i * i <= n:<\/p>\n
        if n % i == 0 or n % (i + 2) == 0:<\/p>\n
            return False<\/p>\n
        i += 6<\/p>\n
    return True<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5<\/h3>\n<\/p>\n
\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u7528\u4e8e\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u627e\u51fa\u6240\u6709\u8d28\u6570\u3002\u5176\u57fa\u672c\u601d\u8def\u662f\u901a\u8fc7\u8fed\u4ee3\u5730\u6807\u8bb0\u975e\u8d28\u6570\u6765\u7b5b\u9009\u51fa\u8d28\u6570\u3002<\/p>\n<\/p>\n
2.1 \u57fa\u672c\u539f\u7406<\/h4>\n<\/p>\n
    \n
  1. \u521b\u5efa\u4e00\u4e2a\u4ece 2 \u5230 ( n ) \u7684\u6570\u7ec4\u3002<\/li>\n
  2. \u4ece\u7b2c\u4e00\u4e2a\u8d28\u6570 2 \u5f00\u59cb\uff0c\u5c06\u6240\u6709 2 \u7684\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\u3002<\/li>\n
  3. \u627e\u5230\u4e0b\u4e00\u4e2a\u672a\u6807\u8bb0\u7684\u6570\uff0c\u5c06\u5176\u6240\u6709\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\u3002<\/li>\n
  4. \u91cd\u590d\u6b65\u9aa4 2 \u548c 3\uff0c\u76f4\u5230\u904d\u5386\u5230 ( \\sqrt{n} ) \u4e3a\u6b62\u3002<\/li>\n
  5. \u5269\u4e0b\u672a\u6807\u8bb0\u7684\u6570\u5373\u4e3a\u8d28\u6570\u3002<\/li>\n<\/ol>\n
    2.2 \u5b9e\u73b0\u4ee3\u7801<\/h4>\n<\/p>\n
    def sieve_of_eratosthenes(n):<\/p>\n
        is_prime = [True] * (n + 1)<\/p>\n
        p = 2<\/p>\n
        while p * p <= n:<\/p>\n
            if is_prime[p]:<\/p>\n
                for i in range(p * p, n + 1, p):<\/p>\n
                    is_prime[i] = False<\/p>\n
            p += 1<\/p>\n
        prime_numbers = [p for p in range(2, n + 1) if is_prime[p]]<\/p>\n
        return prime_numbers<\/p>\n
    <\/code><\/pre>\n<\/p>\n
    \u4e09\u30016k\u00b11\u4f18\u5316\u6cd5<\/h3>\n<\/p>\n
    6k\u00b11\u4f18\u5316\u6cd5\u662f\u57fa\u4e8e\u6570\u8bba\u7684\u6027\u8d28\u6765\u51cf\u5c11\u5224\u65ad\u6b21\u6570\u7684\u4e00\u79cd\u65b9\u6cd5\u3002\u5176\u57fa\u672c\u601d\u60f3\u662f\u9664\u4e86 2 \u548c 3 \u4e4b\u5916\uff0c\u6240\u6709\u8d28\u6570\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a 6k\u00b11 \u7684\u5f62\u5f0f\u3002<\/p>\n<\/p>\n
    3.1 \u57fa\u672c\u539f\u7406<\/h4>\n<\/p>\n
      \n
    1. \u9664\u4e86 2 \u548c 3 \u5916\uff0c\u6240\u6709\u8d28\u6570\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a 6k\u00b11 \u7684\u5f62\u5f0f\u3002<\/li>\n
    2. \u904d\u5386\u4ece 5 \u5f00\u59cb\u7684\u6240\u6709 6k\u00b11 \u7684\u6570\uff0c\u68c0\u67e5\u662f\u5426\u4e3a\u8d28\u6570\u3002<\/li>\n<\/ol>\n
      3.2 \u5b9e\u73b0\u4ee3\u7801<\/h4>\n<\/p>\n
      def is_prime_6k(n):<\/p>\n
          if n <= 1:<\/p>\n
              return False<\/p>\n
          if n <= 3:<\/p>\n
              return True<\/p>\n
          if n % 2 == 0 or n % 3 == 0:<\/p>\n
              return False<\/p>\n
          i = 5<\/p>\n
          while i * i <= n:<\/p>\n
              if n % i == 0 or n % (i + 2) == 0:<\/p>\n
                  return False<\/p>\n
              i += 6<\/p>\n
          return True<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u56db\u3001\u7efc\u5408\u6bd4\u8f83<\/h3>\n<\/p>\n
      \u4ee5\u4e0a\u4e09\u79cd\u65b9\u6cd5\u5404\u6709\u4f18\u7f3a\u70b9\uff0c\u9002\u7528\u4e8e\u4e0d\u540c\u7684\u573a\u666f\u3002<\/p>\n<\/p>\n
      4.1 \u8bd5\u9664\u6cd5<\/h4>\n<\/p>\n
      \u4f18\u70b9\uff1a\u7b80\u5355\u6613\u61c2\uff0c\u5bb9\u6613\u5b9e\u73b0\u3002<\/p>\n
      \u7f3a\u70b9\uff1a\u6548\u7387\u8f83\u4f4e\uff0c\u9002\u5408\u5c0f\u8303\u56f4\u5185\u7684\u8d28\u6570\u5224\u65ad\u3002<\/p>\n<\/p>\n
      4.2 \u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5<\/h4>\n<\/p>\n
      \u4f18\u70b9\uff1a\u9002\u5408\u5927\u8303\u56f4\u5185\u7684\u8d28\u6570\u7b5b\u9009\uff0c\u6548\u7387\u9ad8\u3002<\/p>\n
      \u7f3a\u70b9\uff1a\u9700\u8981\u8f83\u5927\u7684\u5185\u5b58\u7a7a\u95f4\uff0c\u9002\u5408\u4e00\u6b21\u6027\u627e\u51fa\u8f83\u591a\u8d28\u6570\u7684\u60c5\u51b5\u3002<\/p>\n<\/p>\n
      4.3 6k\u00b11\u4f18\u5316\u6cd5<\/h4>\n<\/p>\n
      \u4f18\u70b9\uff1a\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u63d0\u9ad8\u4e86\u6548\u7387\uff0c\u9002\u5408\u4e2d\u7b49\u8303\u56f4\u7684\u8d28\u6570\u5224\u65ad\u3002<\/p>\n
      \u7f3a\u70b9\uff1a\u5b9e\u73b0\u7a0d\u590d\u6742\uff0c\u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\uff0c\u6548\u7387\u63d0\u5347\u6709\u9650\u3002<\/p>\n<\/p>\n
      \u4e94\u3001\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u4f18\u5316<\/h3>\n<\/p>\n
      \u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u4ee5\u7ed3\u5408\u591a\u79cd\u65b9\u6cd5\u8fdb\u884c\u4f18\u5316\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u5148\u4f7f\u7528\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5\u627e\u51fa\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u8d28\u6570\uff0c\u7136\u540e\u4f7f\u7528\u8bd5\u9664\u6cd5\u62166k\u00b11\u4f18\u5316\u6cd5\u8fdb\u884c\u8fdb\u4e00\u6b65\u7684\u5224\u65ad\u3002<\/p>\n<\/p>\n
      5.1 \u7ec4\u5408\u65b9\u6cd5<\/h4>\n<\/p>\n
      def is_prime_combined(n, prime_list):<\/p>\n
          if n <= 1:<\/p>\n
              return False<\/p>\n
          if n in prime_list:<\/p>\n
              return True<\/p>\n
          for prime in prime_list:<\/p>\n
              if prime * prime > n:<\/p>\n
                  break<\/p>\n
              if n % prime == 0:<\/p>\n
                  return False<\/p>\n
          return True<\/p>\n
      Example usage:<\/strong><\/h2>\n
      prime_list = sieve_of_eratosthenes(100)<\/p>\n
      print(is_prime_combined(101, prime_list))  # True<\/p>\n
      print(is_prime_combined(102, prime_list))  # False<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      5.2 \u5e76\u884c\u8ba1\u7b97<\/h4>\n<\/p>\n
      \u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\uff0c\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u5e76\u884c\u8ba1\u7b97\u6765\u63d0\u9ad8\u6548\u7387\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u7ebf\u7a0b\u6216\u591a\u8fdb\u7a0b\u6765\u5e76\u884c\u5316\u7b5b\u9009\u548c\u8bd5\u9664\u8fc7\u7a0b\u3002<\/p>\n<\/p>\n
      \u516d\u3001Python\u5185\u7f6e\u5e93\u7684\u4f7f\u7528<\/h3>\n<\/p>\n
      Python\u5185\u7f6e\u5e93\u5982 sympy<\/code> \u4e5f\u63d0\u4f9b\u4e86\u8d28\u6570\u5224\u65ad\u7684\u529f\u80fd\uff0c\u53ef\u4ee5\u7b80\u5316\u5b9e\u73b0\u3002<\/p>\n<\/p>\n
      6.1 \u4f7f\u7528 sympy \u5e93<\/h4>\n<\/p>\n
      from sympy import isprime<\/p>\n
      print(isprime(101))  # True<\/p>\n
      print(isprime(102))  # False<\/p>\n
      <\/code><\/pre>\n<\/p>\n
      \u4e03\u3001\u603b\u7ed3<\/h3>\n<\/p>\n
      \u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u53ef\u4ee5\u6839\u636e\u5177\u4f53\u7684\u9700\u6c42\u548c\u5e94\u7528\u573a\u666f\u3002\u8bd5\u9664\u6cd5\u9002\u5408\u5c0f\u8303\u56f4\u5185\u7684\u8d28\u6570\u5224\u65ad\uff0c\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5\u9002\u5408\u5927\u8303\u56f4\u5185\u7684\u8d28\u6570\u7b5b\u9009\uff0c6k\u00b11\u4f18\u5316\u6cd5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u63d0\u9ad8\u4e86\u6548\u7387\u3002\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u4ee5\u7ed3\u5408\u591a\u79cd\u65b9\u6cd5\u8fdb\u884c\u4f18\u5316\uff0c\u5e76\u5229\u7528\u5e76\u884c\u8ba1\u7b97\u548c\u5185\u7f6e\u5e93\u6765\u8fdb\u4e00\u6b65\u63d0\u9ad8\u6548\u7387\u3002<\/p>\n<\/p>\n
      \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
       \u5982\u4f55\u786e\u5b9a\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\uff1f<\/strong>
      \u8981\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\uff0c\u9996\u5148\u9700\u8981\u4e86\u89e3\u8d28\u6570\u7684\u5b9a\u4e49\uff1a\u8d28\u6570\u662f\u6307\u5927\u4e8e1\u7684\u81ea\u7136\u6570\uff0c\u9664\u4e861\u548c\u5b83\u672c\u8eab\u5916\uff0c\u6ca1\u6709\u5176\u4ed6\u7684\u56e0\u6570\u3002\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u68c0\u67e5\u8be5\u6570\u662f\u5426\u80fd\u591f\u88ab2\u5230\u5176\u5e73\u65b9\u6839\u4e4b\u95f4\u7684\u4efb\u4f55\u6574\u6570\u6574\u9664\u3002\u5982\u679c\u4e0d\u80fd\u88ab\u8fd9\u4e9b\u6570\u6574\u9664\uff0c\u5219\u8be5\u6570\u4e3a\u8d28\u6570\u3002<\/p>\n
      \u5728Python\u4e2d\u6709\u54ea\u4e9b\u5e38\u7528\u7684\u8d28\u6570\u5224\u65ad\u7b97\u6cd5\uff1f<\/strong>
      \u5728Python\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u7b97\u6cd5\u6765\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u3002\u5176\u4e2d\u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u5faa\u73af\u904d\u5386\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\uff0c\u68c0\u67e5\u662f\u5426\u6709\u6574\u9664\u7684\u60c5\u51b5\u3002\u6b64\u5916\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u66f4\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u6bd4\u5982\u8bd5\u9664\u6cd5\u548c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\uff0c\u6765\u4f18\u5316\u8d28\u6570\u5224\u65ad\u7684\u8fc7\u7a0b\u3002<\/p>\n
      \u5982\u4f55\u5728Python\u4e2d\u5b9e\u73b0\u8d28\u6570\u5224\u65ad\u7684\u4ee3\u7801\uff1f<\/strong>
      \u4e00\u4e2a\u7b80\u5355\u7684\u8d28\u6570\u5224\u65ad\u51fd\u6570\u53ef\u4ee5\u5982\u4e0b\u5b9e\u73b0\uff1a  <\/p>\n
      def is_prime(n):\n    if n <= 1:\n        return False\n    for i in range(2, int(n**0.5) + 1):\n        if n % i == 0:\n            return False\n    return True\n<\/code><\/pre>\n
      \u4f7f\u7528\u8fd9\u4e2a\u51fd\u6570\u65f6\uff0c\u53ea\u9700\u4f20\u5165\u4e00\u4e2a\u6574\u6570\uff0c\u51fd\u6570\u5c06\u8fd4\u56deTrue<\/code>\u6216False<\/code>\uff0c\u8868\u793a\u8be5\u6570\u662f\u5426\u4e3a\u8d28\u6570\u3002<\/p>\n
      Python\u4e2d\u662f\u5426\u6709\u73b0\u6210\u7684\u5e93\u53ef\u4ee5\u5224\u65ad\u8d28\u6570\uff1f<\/strong>
      \u662f\u7684\uff0cPython\u7684sympy<\/code>\u5e93\u63d0\u4f9b\u4e86\u4e00\u4e2a\u975e\u5e38\u65b9\u4fbf\u7684\u51fd\u6570isprime()<\/code>\uff0c\u53ef\u4ee5\u7528\u6765\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u3002\u4f7f\u7528\u8fd9\u4e2a\u5e93\u65f6\uff0c\u53ea\u9700\u5148\u5b89\u88c5sympy<\/code>\uff0c\u7136\u540e\u8c03\u7528isprime()<\/code>\u51fd\u6570\u5373\u53ef\u3002\u4f8b\u5982\uff1a  <\/p>\n
      from sympy import isprime\nprint(isprime(7))  # \u8f93\u51fa True\n<\/code><\/pre>\n
      \u8fd9\u4f7f\u5f97\u5224\u65ad\u8d28\u6570\u53d8\u5f97\u66f4\u52a0\u7b80\u5355\u548c\u5feb\u6377\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"Python \u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u8d28\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5e38\u89c1\u7684\u65b9\u6cd5\u5305\u62ec\uff1a\u8bd5\u9664\u6cd5\u3001\u57c3\u62c9\u6258\u8272\u5c3c\u7b5b\u6cd5\u30016k\u00b11\u4f18\u5316\u6cd5\u3002\u6211\u4eec\u53ef […]","protected":false},"author":3,"featured_media":1128255,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1128247"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1128247"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1128247\/revisions"}],"predecessor-version":[{"id":1128257,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1128247\/revisions\/1128257"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1128255"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1128247"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1128247"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1128247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}