滴水恩情 发表于 2024-2-20 21:38:57

MySQL-07.单行函数

C-07.单行函数

1.函数的理解

1.1 什么是函数

函数在计算机语言中的使用贯穿始终,函数的作用是什么呢?它可以把我们经常使用的代码封装起来,需要的时候直接调用即可。这样即提高了代码效率,又提高了可维护性。在SQL中我们也可以使用函数对检索出的数据进行函数操作。使用这函数,可以极大地提高用户对数据库的管理效率。
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216002855376-119274384.jpg
从函数的定义角度出发,我们可以将函数分成内置函数和自定义函数。在SQL语言中,同样也包括了内置函数的自定义函数。内置函数是系统内置的通用函数,而自定义函数是我们根据自己的需要编写的,本章和下一章讲解的是SQL的内置函数。
1.2 不同DBMS的函数的差异

我们在使用SQL语言时,是和各种不同的DBMS打交道。DBMS之间的差异性很大,远大于同一个语言不同版本之间的差异。实际上,只是很少的函数是被DBMS同时支持的。比如,大多数DBMS使用(||)或(+)来做拼接符,而在MySQL中的字符串拼接函数为concat()。大部分DBMS会有自己特定的函数,这就意味着采用SQL函数的代码可移植性是很差的,因此在使用函数的时候需要特别注意。
1.3 MySQL的内置函数分类

MySQL提供了丰富的内置函数,这些函数使得数据的维护与管理更加方便,能够更好的提供数据的分析和统计能力,在一定程度上提高了开发人员进行数据分析与统计的效率。
MySQL提供的内置函数从实现的功能角度可以分为数值函数,字符串函数,日期与时间函数,流程控制函数,加密与解密函数,获取MySQL信息函数,聚合函数等。也可以分为单行函数,聚合函数(或分组函数)。
两种SQL函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216002915856-2075514074.jpg
单行函数


[*]操作数据对象
[*]接收参数返回一个结果
[*]只对一行进行变换
[*]每行返回一个结果
[*]可以嵌套
[*]参数可以一列或一个值
2.数值函数

2.1 基本函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216002936867-1004076518.jpg
举例:
SELECT ABS(-10.1),SIGN(-23),SIGN(20),PI(),CEIL(-41.2),CEILING(20.8),FLOOR(20.8),FLOOR(-41.2),MOD(12,5)
FROM dual;https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003013524-771213425.jpg
SELECT RAND(),RAND(),RAND(10),RAND(10),RAND(-2),RAND(-2) FROM dual;https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003029390-290626891.jpg
mysql> SELECT ROUND(10.5),ROUND(10.224,2),ROUND(13.325,-1),TRUNCATE(10.66,1),TRUNCATE(12.66,-1) FROM dual;
+-------------+-----------------+------------------+-------------------+--------------------+
| ROUND(10.5) | ROUND(10.224,2) | ROUND(13.325,-1) | TRUNCATE(10.66,1) | TRUNCATE(12.66,-1) |
+-------------+-----------------+------------------+-------------------+--------------------+
|          11 |         10.22 |               10 |            10.6 |               10 |
+-------------+-----------------+------------------+-------------------+--------------------+
1 row in set (0.00 sec)2.2 角度与弧度互换函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003103721-1420582097.jpg
mysql> SELECT RADIANS(30),RADIANS(60),RADIANS(90),DEGREES(2*PI()),DEGREES(RADIANS(90)) FROM dual;
+--------------------+--------------------+--------------------+-----------------+----------------------+
| RADIANS(30)      | RADIANS(60)      | RADIANS(90)      | DEGREES(2*PI()) | DEGREES(RADIANS(90)) |
+--------------------+--------------------+--------------------+-----------------+----------------------+
| 0.5235987755982988 | 1.0471975511965976 | 1.5707963267948966 |             360 |                   90 |
+--------------------+--------------------+--------------------+-----------------+----------------------+
1 row in set (0.00 sec)2.3 三角函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003129765-1282809832.jpg
举例:
ATAN2(m,n)函数返回两个参数的反正切值。与ATAN(x)函数相比,ATAN2(m,n)需要两个参数。例如有两个点point(x1,y1)和point(x2,y2),使用ATAN(x)函数计算反正切值为ATAN((y2-y1)/(x2-x1)),使用ATAN2(m,n)计算反正切值为ATAN2(x2-x1,y2-y1)。
注意分母不能为0的情况。
mysql> SELECTSIN(RADIANS(30)),DEGREES(ASIN(1)),TAN(RADIANS(45)),DEGREES(ATAN(1)),DEGREES(ATAN2(1,1))
    -> FROM dual;
+---------------------+------------------+--------------------+------------------+---------------------+
| SIN(RADIANS(30))    | DEGREES(ASIN(1)) | TAN(RADIANS(45))   | DEGREES(ATAN(1)) | DEGREES(ATAN2(1,1)) |
+---------------------+------------------+--------------------+------------------+---------------------+
| 0.49999999999999994 |               90 | 0.9999999999999999 |               45 |                  45 |
+---------------------+------------------+--------------------+------------------+---------------------+
1 row in set (0.00 sec)2.4 指数与对数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003320861-1261898637.jpg
mysql> SELECT POW(2,3),POWER(2,3),EXP(3),LN(EXP(2)),LOG10(100),LOG2(64) FROM dual;
+----------+------------+--------------------+------------+------------+----------+
| POW(2,3) | POWER(2,3) | EXP(3)             | LN(EXP(2)) | LOG10(100) | LOG2(64) |
+----------+------------+--------------------+------------+------------+----------+
|      8 |          8 | 20.085536923187668 |          2 |          2 |      6 |
+----------+------------+--------------------+------------+------------+----------+
1 row in set (0.00 sec)2.5 进制间的转换

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003342480-1303118647.jpg
mysql> SELECT BIN(12),HEX(12),OCT(12),CONV(10,2,8) FROM dual;
+---------+---------+---------+--------------+
| BIN(12) | HEX(12) | OCT(12) | CONV(10,2,8) |
+---------+---------+---------+--------------+
| 1100    | C       | 14      | 2            |
+---------+---------+---------+--------------+
1 row in set (0.00 sec)3.字符串函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003405615-1750457626.jpg
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003408973-1636629804.jpg
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003411735-1750735105.jpg
举例
mysql> SELECT FIELD('mm','hello','mm','asmr'),FIND_IN_SET('mm','hello,mm,asmr')
    -> FROM dual;
+---------------------------------+-----------------------------------+
| FIELD('mm','hello','mm','asmr') | FIND_IN_SET('mm','hello,mm,asmr') |
+---------------------------------+-----------------------------------+
|                               2 |                                 2 |
+---------------------------------+-----------------------------------+
1 row in set (0.00 sec)

mysql> SELECT REVERSE('asmr'),NULLIF('mysql','mysql'),NULLIF('mysql','mysqld')
    -> FROM dual;
+-----------------+-------------------------+--------------------------+
| REVERSE('asmr') | NULLIF('mysql','mysql') | NULLIF('mysql','mysqld') |
+-----------------+-------------------------+--------------------------+
| rmsa            | NULL                  | mysql                  |
+-----------------+-------------------------+--------------------------+
1 row in set (0.00 sec)4.日期和时间函数

4.1 获取日期,时间

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003448732-810198192.jpg
举例:
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003501410-1251343766.jpg
4.2 日期与时间戳的转换

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003519587-1957259248.jpg
mysql> SELECT UNIX_TIMESTAMP(),FROM_UNIXTIME(now()),FROM_UNIXTIME(UNIX_TIMESTAMP()) FROM dual;
+------------------+----------------------+---------------------------------+
| UNIX_TIMESTAMP() | FROM_UNIXTIME(now()) | FROM_UNIXTIME(UNIX_TIMESTAMP()) |
+------------------+----------------------+---------------------------------+
|       1702562470 | NULL               | 2023-12-14 22:01:10             |
+------------------+----------------------+---------------------------------+
1 row in set (0.00 sec)4.3 获取月份,天数,星期数等函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003543814-906474733.jpg
mysql> SELECT YEAR(CURDATE()),MONTH(CURDATE()),DAY(CURDATE()),HOUR(CURTIME()),MINUTE(NOW()),SECOND(SYSDATE()) FROM dual;
+-----------------+------------------+----------------+-----------------+---------------+-------------------+
| YEAR(CURDATE()) | MONTH(CURDATE()) | DAY(CURDATE()) | HOUR(CURTIME()) | MINUTE(NOW()) | SECOND(SYSDATE()) |
+-----------------+------------------+----------------+-----------------+---------------+-------------------+
|            2023 |               12 |             14 |            22 |             5 |               8 |
+-----------------+------------------+----------------+-----------------+---------------+-------------------+
1 row in set (0.00 sec)

mysql> SELECT MONTHNAME(now()),DAYNAME(now()),WEEKDAY(CURDATE()),QUARTER(SYSDATE()),WEEK(now()),DAYOFYEAR(now()),DAYOFMONTH(now()),DAYOFWEEK(now()) FROM dual;
+------------------+----------------+--------------------+--------------------+-------------+------------------+-------------------+------------------+
| MONTHNAME(now()) | DAYNAME(now()) | WEEKDAY(CURDATE()) | QUARTER(SYSDATE()) | WEEK(now()) | DAYOFYEAR(now()) | DAYOFMONTH(now()) | DAYOFWEEK(now()) |
+------------------+----------------+--------------------+--------------------+-------------+------------------+-------------------+------------------+
| December         | Thursday       |                  3 |                  4 |          50 |            348 |                14 |                5 |
+------------------+----------------+--------------------+--------------------+-------------+------------------+-------------------+------------------+
1 row in set (0.00 sec)4.4 日期的操作函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003646905-241602635.jpg
mysql> SELECT EXTRACT(MINUTE FROM now()),EXTRACT(WEEK FROM NOW()),EXTRACT(QUARTER FROM NOW()),EXTRACT(MINUTE_SECOND FROM now()) FROM dual;
+----------------------------+--------------------------+-----------------------------+-----------------------------------+
| EXTRACT(MINUTE FROM now()) | EXTRACT(WEEK FROM NOW()) | EXTRACT(QUARTER FROM NOW()) | EXTRACT(MINUTE_SECOND FROM now()) |
+----------------------------+--------------------------+-----------------------------+-----------------------------------+
|                         13 |                     50 |                           4 |                              1311 |
+----------------------------+--------------------------+-----------------------------+-----------------------------------+
1 row in set (0.00 sec)4.5 时间和秒钟转换的函数

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003715783-1054655842.jpg
mysql> SELECT TIME_TO_SEC(NOW());
+--------------------+
| TIME_TO_SEC(NOW()) |
+--------------------+
|            85290 |
+--------------------+
1 row in set (0.00 sec)

mysql> SELECT SEC_TO_TIME(85290);
+--------------------+
| SEC_TO_TIME(85290) |
+--------------------+
| 23:41:30         |
+--------------------+
1 row in set (0.00 sec)4.6 计算日期和时间的函数

第一组

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003748414-1097523837.jpg
# now() 也可以是代表日期的常量,如'2023-12-14 23:46:20'
mysql> SELECT DATE_ADD(NOW(),INTERVAL 1 DAY) AS col1,ADDDATE(NOW(),INTERVAL 1 SECOND) AS col2 FROM dual;
+---------------------+---------------------+
| col1                | col2                |
+---------------------+---------------------+
| 2023-12-15 23:46:38 | 2023-12-14 23:46:39 |
+---------------------+---------------------+
1 row in set (0.00 sec)

mysql> SELECT DATE_SUB(NOW(),INTERVAL 1 DAY) AS col1,SUBDATE(NOW(),INTERVAL 1 SECOND) AS col2 FROM dual;
+---------------------+---------------------+
| col1                | col2                |
+---------------------+---------------------+
| 2023-12-13 23:47:14 | 2023-12-14 23:47:13 |
+---------------------+---------------------+
1 row in set (0.00 sec)第二组

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216003919524-943536023.jpg
mysql> SELECT ADDTIME(NOW(),20),SUBTIME(NOW(),30),SUBTIME(NOW(),'1:1:3') FROM dual;
+---------------------+---------------------+------------------------+
| ADDTIME(NOW(),20)   | SUBTIME(NOW(),30)   | SUBTIME(NOW(),'1:1:3') |
+---------------------+---------------------+------------------------+
| 2023-12-14 23:52:38 | 2023-12-14 23:51:48 | 2023-12-14 22:51:15    |
+---------------------+---------------------+------------------------+
1 row in set (0.00 sec)

mysql> SELECT DATEDIFF(NOW(),'2022-10-01'),TIMEDIFF(NOW(),'2023-10-01 00:00:00'),FROM_DAYS(366) FROM dual;
+------------------------------+---------------------------------------+----------------+
| DATEDIFF(NOW(),'2022-10-01') | TIMEDIFF(NOW(),'2023-10-01 00:00:00') | FROM_DAYS(366) |
+------------------------------+---------------------------------------+----------------+
|                        439 | 838:59:59                           | 0001-01-01   |
+------------------------------+---------------------------------------+----------------+
1 row in set, 1 warning (0.00 sec)

mysql> SELECT TO_DAYS('0000-12-14'),LAST_DAY(NOW()),MAKEDATE(YEAR(NOW()),122) FROM dual;
+-----------------------+-----------------+---------------------------+
| TO_DAYS('0000-12-14') | LAST_DAY(NOW()) | MAKEDATE(YEAR(NOW()),122) |
+-----------------------+-----------------+---------------------------+
|                   348 | 2023-12-31      | 2023-05-02                |
+-----------------------+-----------------+---------------------------+
1 row in set (0.00 sec)

mysql> SELECT PERIOD_ADD(202011,10),MAKETIME(10,25,56) FROM dual;
+-----------------------+--------------------+
| PERIOD_ADD(202011,10) | MAKETIME(10,25,56) |
+-----------------------+--------------------+
|                202109 | 10:25:56         |
+-----------------------+--------------------+
1 row in set (0.00 sec)注意,图中关于PERIOD_AD输入不同的参数可能有问题,不推荐使用
查询7天内新增用户有多少?
SELECT COUNT(*) AS num FROM user WHERE TO_DAYS(NOW()) - TO_DAYS(regist_time) <= 7;注意,没有STR_TO_TIME函数。
5.流程控制函数

流程控制函数可以根据不同的条件,执行不同的处理流程,可以在SQL语句中,实现不同的条件选择。MySQL中的流程处理函数主要包括IF(),IFNULL()和CASE()函数。
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216004320532-1755834864.jpg
mysql> SELECT TIME_FORMAT(CURTIME(),'%H:%i:%s'),DATE_FORMAT(CURDATE(),'%Y-%m-%d') FROM dual;
+-----------------------------------+-----------------------------------+
| TIME_FORMAT(CURTIME(),'%H:%i:%s') | DATE_FORMAT(CURDATE(),'%Y-%m-%d') |
+-----------------------------------+-----------------------------------+
| 23:02:36                        | 2023-12-15                        |
+-----------------------------------+-----------------------------------+
1 row in set (0.00 sec)

mysql> SELECT GET_FORMAT(DATE,'USA'),GET_FORMAT(TIME,'USA') FROM dual;
+------------------------+------------------------+
| GET_FORMAT(DATE,'USA') | GET_FORMAT(TIME,'USA') |
+------------------------+------------------------+
| %m.%d.%Y               | %h:%i:%s %p            |
+------------------------+------------------------+
1 row in set (0.00 sec)

mysql> SELECT STR_TO_DATE('2021-01-05 00:00:00','%Y-%m-%d') FROM dual;
+-----------------------------------------------+
| STR_TO_DATE('2021-01-05 00:00:00','%Y-%m-%d') |
+-----------------------------------------------+
| 2021-01-05                                    |
+-----------------------------------------------+
1 row in set, 1 warning (0.00 sec)

mysql> SELECT STR_TO_DATE('2021-01-05 00:00:00','%Y-%m-%d %H:%i:%s') FROM dual;
+--------------------------------------------------------+
| STR_TO_DATE('2021-01-05 00:00:00','%Y-%m-%d %H:%i:%s') |
+--------------------------------------------------------+
| 2021-01-05 00:00:00                                    |
+--------------------------------------------------------+
1 row in set (0.00 sec6.加密与解密函数

加密与解密函数主要用于对数据库中的数据进行加密和解密处理,以防止数据被他人窃取,这些函数在保证数据库安全时非常有用。
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216004310544-897323989.jpg
mysql> SELECT IF(1 > 0,'正确','错误'),IFNULL(null,'Hello,World') FROM dual;
+-------------------------+----------------------------+
| IF(1 > 0,'正确','错误') | IFNULL(null,'Hello,World') |
+-------------------------+----------------------------+
| 正确                  | Hello,World                |
+-------------------------+----------------------------+
1 row in set (0.00 sec)

mysql> SELECT CASE WHEN 1 > 0 THEN '第一个成立' WHEN 2 > 0 THEN '第二个成立' ELSE '前两个都不成立' END
    -> ;
+------------------------------------------------------------------------------------------+
| CASE WHEN 1 > 0 THEN '第一个成立' WHEN 2 > 0 THEN '第二个成立' ELSE '前两个都不成立' END |
+------------------------------------------------------------------------------------------+
| 第一个成立                                                                               |
+------------------------------------------------------------------------------------------+
1 row in set (0.00 sec)

mysql> SELECT CASE 1
    -> WHEN 1 THEN '值是1'
    -> WHEN 2 THEN '值是2'
    -> ELSE '值是N'
    -> END;
+-----------------------------------------------------------------+
| CASE 1
WHEN 1 THEN '值是1'
WHEN 2 THEN '值是2'
ELSE '值是N'
END |
+-----------------------------------------------------------------+
| 值是1                                                         |
+-----------------------------------------------------------------+
1 row in set (0.00 sec)

mysql> SELECT last_name,salary,department_id,CASE department_id WHEN 10 THEN 1.1 * salary
    -> WHEN 20 THEN (1.2 * salary) WHEN 30 THEN (1.3 * salary) ELSE salary END '薪水'
    -> FROM employees;
+-------------+----------+---------------+----------+
| last_name   | salary   | department_id | 薪水   |
+-------------+----------+---------------+----------+
| King      | 24000.00 |            90 | 24000.00 |
| Kochhar   | 17000.00 |            90 | 17000.00 |
| De Haan   | 17000.00 |            90 | 17000.00 |
...
| Mavris      |6500.00 |            40 |6500.00 |
| Baer      | 10000.00 |            70 | 10000.00 |
| Higgins   | 12000.00 |         110 | 12000.00 |
| Gietz       |8300.00 |         110 |8300.00 |
+-------------+----------+---------------+----------+
107 rows in set (0.00 sec)注意password函数在MySQL8.0后已经取消支持了。上述时在5.7版本下执行的。
mysql> SELECT PASSWORD('wind');
+-------------------------------------------+
| PASSWORD('wind')                        |
+-------------------------------------------+
| *E04A13B4BCD1DCBE73B56F656D27615E2C2BFE55 |
+-------------------------------------------+
1 row in set, 1 warning (0.00 sec)8.0环境下的执行会报错。
mysql> SELECT PASSWORD('wind');
ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '('wind')' at line 1MD5()和SHA(),5.7和8.0都支持。
ENCODE()和DECODE()也都是在8.0中不支持。
7.MySQL信息函数

MySQL内置了一些可以查询MySQL信息的函数,这些函数主要用于帮助数据库开发或运维人员更好地维护数据库。
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216004527951-56094419.jpg
mysql> SELECT MD5('wind');
+----------------------------------+
| MD5('wind')                      |
+----------------------------------+
| 7e25b972e192b01004b62346ee9975a5 |
+----------------------------------+
1 row in set (0.00 sec)
mysql> SELECT SHA('WIND');
+------------------------------------------+
| SHA('WIND')                              |
+------------------------------------------+
| c514a747e8f0bc9e5d9beba8fe62416cc7b2a66e |
+------------------------------------------+
1 row in set (0.00 sec)8.其他函数

MySQL有些函数,无法进行具体的分类,但是使用较为频繁。
https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216004512999-1578464521.jpg
mysql> SELECT DATABASE();
+------------+
| DATABASE() |
+------------+
| atguigudb|
+------------+
1 row in set (0.00 sec)

mysql> SELECT USER(),CURRENT_USER(),SYSTEM_USER(),SESSION_USER();
+----------------+----------------+----------------+----------------+
| USER()         | CURRENT_USER() | SYSTEM_USER()| SESSION_USER() |
+----------------+----------------+----------------+----------------+
| root@localhost | root@localhost | root@localhost | root@localhost |
+----------------+----------------+----------------+----------------+
1 row in set (0.00 sec)

mysql> SELECT CHARSET('abc'),COLLATION('abc');
+----------------+------------------+
| CHARSET('abc') | COLLATION('abc') |
+----------------+------------------+
| gbk            | gbk_chinese_ci   |
+----------------+------------------+
1 row in set (0.00 sec)练习

使用的表结构

https://img2023.cnblogs.com/blog/2883613/202312/2883613-20231216004638271-1911775152.jpg
# 如果n的值小于或等于0,只保留整数
mysql> SELECT FORMAT(123.12,2),FORMAT(123.354,2),FORMAT(12.546,-1);
+------------------+-------------------+-------------------+
| FORMAT(123.12,2) | FORMAT(123.354,2) | FORMAT(12.546,-1) |
+------------------+-------------------+-------------------+
| 123.12         | 123.35            | 13                |
+------------------+-------------------+-------------------+
1 row in set (0.00 sec)

mysql> SELECT CONV(10,10,2),CONV(10,10,16),CONV(NULL,10,2);
+---------------+----------------+-----------------+
| CONV(10,10,2) | CONV(10,10,16) | CONV(NULL,10,2) |
+---------------+----------------+-----------------+
| 1010          | A            | NULL            |
+---------------+----------------+-----------------+
1 row in set (0.00 sec)

#计算公式192 * 256^3 + 168 * 256^2 + 0 * 256 + 130 = 3232235650
mysql> SELECT INET_ATON('192.168.0.130');
+----------------------------+
| INET_ATON('192.168.0.130') |
+----------------------------+
|               3232235650 |
+----------------------------+
1 row in set (0.00 sec)

mysql> SELECT INET_NTOA(3232235650);
+-----------------------+
| INET_NTOA(3232235650) |
+-----------------------+
| 192.168.0.130         |
+-----------------------+
1 row in set (0.00 sec)

mysql> SELECT BENCHMARK(10000,MD5('WIND'));
+------------------------------+
| BENCHMARK(10000,MD5('WIND')) |
+------------------------------+
|                            0 |
+------------------------------+
1 row in set (0.00 sec)

mysql> SELECT CHARSET('mysql'),CHARSET(CONVERT('mysql' USING 'utf8'));
+------------------+----------------------------------------+
| CHARSET('mysql') | CHARSET(CONVERT('mysql' USING 'utf8')) |
+------------------+----------------------------------------+
| gbk            | utf8mb3                              |
+------------------+----------------------------------------+
1 row in set, 1 warning (0.00 sec)只是为了记录自己的学习历程,且本人水平有限,不对之处,请指正。

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