Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
| J   | K   | L   |    M |    N |    O | P         | Q          |
|:----|:----|:----|-----:|-----:|-----:|:----------|:-----------|
| A   | M   | U   | 1872 | 1875 |    3 | 3/1/1872  | 12/31/1875 |
| A   | M   | U   | 1874 | 1875 |    1 | 3/1/1874  | 12/31/1875 |
| A   | M   | U   | 1874 | 1882 |    8 | 3/1/1874  | 12/31/1882 |
| A   | M   | U   | 1882 | 1887 |    5 | 3/1/1882  | 12/31/1887 |
| A   | M   | U   | 1885 | 1887 |    2 | 3/1/1885  | 12/31/1887 |
| A   | M   | U   | 1885 | 1887 |    2 | 3/1/1885  | 12/31/1887 |
| A   | M   | U   | 1885 | 1900 |   15 | 3/1/1885  | 12/31/1900 |
| A   | M   | U   | 1887 | 1890 |    3 | 3/1/1887  | 12/31/1890 |
| A   | M   | U   | 1889 | 1892 |    3 | 3/1/1889  | 12/31/1892 |
| A   | M   | U   | 1891 | 1896 |    5 | 3/1/1891  | 12/31/1896 |
| A   | M   | U   | 1893 | 1899 |    6 | 3/1/1893  | 12/31/1899 |
| A   | M   | U   | 1896 | 1898 |    2 | 3/1/1896  | 12/31/1898 |
| A   | M   | U   | 1899 | 1900 |    1 | 3/1/1899  | 12/31/1900 |
| A   | M   | U   | 1900 | 1900 |    0 | 3/1/1900  | 12/31/1900 |
| A   | M   | U   | 1901 | 1904 |    3 | 3/1/1901  | 12/31/1904 |
| A   | M   | U   | 1901 | 1914 |   13 | 3/1/1901  | 12/31/1914 |
| A   | M   | U   | 1901 | 1921 |   20 | 3/1/1901  | 12/31/1921 |
| A   | M   | U   | 1905 | 1908 |    3 | 3/1/1905  | 12/31/1908 |
| A   | M   | U   | 1909 | 1917 |    8 | 3/1/1909  | 12/31/1917 |
| E   | M   | U   | 1914 | 1932 |   18 | 1/1/1914  | 12/31/1932 |
| E   | M   | U   | 1917 | 1923 |    6 | 1/1/1917  | 12/31/1923 |
| E   | M   | U   | 1921 | 1927 |    6 | 1/1/1921  | 12/31/1927 |
| E   | M   | U   | 1923 | 1923 |    0 | 1/1/1923  | 12/31/1923 |
| E   | M   | U   | 1923 | 1936 |   13 | 1/1/1923  | 12/31/1936 |
| E   | M   | U   | 1928 | 1934 |    6 | 1/1/1928  | 12/31/1934 |
| E   | M   | U   | 1933 | 1936 |    3 | 1/1/1933  | 12/31/1936 |
| E   | M   | U   | 1935 | 1940 |    5 | 1/1/1935  | 12/31/1940 |
| E   | M   | U   | 1936 | 1938 |    2 | 1/1/1936  | 12/31/1938 |
| E   | M   | U   | 1937 | 1942 |    5 | 1/1/1937  | 12/31/1942 |
| E   | M   | U   | 1939 | 1949 |   10 | 1/1/1939  | 12/31/1949 |
| E   | M   | U   | 1941 | 1951 |   10 | 1/1/1941  | 12/31/1951 |
| E   | M   | U   | 1943 | 1943 |    0 | 1/1/1943  | 12/31/1943 |
| E   | M   | U   | 1943 | 1944 |    1 | 1/1/1943  | 12/31/1944 |
| E   | M   | U   | 1944 | 1948 |    4 | 1/1/1944  | 12/31/1948 |
| E   | M   | U   | 1948 | 1948 |    0 | 1/1/1948  | 12/31/1948 |
| E   | M   | U   | 1949 | 1952 |    3 | 1/1/1949  | 12/31/1952 |
| E   | M   | U   | 1949 | 1954 |    5 | 1/1/1949  | 12/31/1954 |
| E   | M   | U   | 1951 | 1958 |    7 | 1/1/1951  | 12/31/1958 |
| E   | M   | U   | 1952 | 1952 |    0 | 1/1/1952  | 12/31/1952 |
| E   | M   | U   | 1952 | 1970 |   18 | 1/1/1952  | 12/31/1970 |
| E   | M   | U   | 1955 | 1966 |   11 | 1/1/1955  | 12/31/1966 |
| E   | M   | D   | 1959 | 1972 |   13 | 1/1/1959  | 12/31/1972 |
| E   | M   | U   | 1967 | 1972 |    5 | 1/1/1967  | 12/31/1972 |
| E   | M   | R   | 1970 | 1975 |    5 | 1/1/1970  | 12/31/1975 |
| E   | M   | D   | 1972 | 1977 |    5 | 1/1/1972  | 12/31/1977 |
| A   | F   | R   | 1975 | 1979 |    4 | 3/1/1975  | 12/31/1979 |
| A   | F   | R   | 1975 | 1981 |    6 | 3/1/1975  | 12/31/1981 |
| A   | M   | D   | 1975 | 1976 |    1 | 3/1/1975  | 12/31/1976 |
| A   | M   | D   | 1976 | 1981 |    5 | 3/1/1976  | 12/31/1981 |
| A   | F   | D   | 1977 | 1983 |    6 | 3/1/1977  | 12/31/1983 |
| A   | F   | D   | 1978 | 1980 |    2 | 3/1/1978  | 12/31/1980 |
| A   | F   | R   | 1979 | 1984 |    5 | 3/1/1979  | 12/31/1984 |
| A   | M   | D   | 1980 | 1984 |    4 | 3/1/1980  | 12/31/1984 |
| A   | M   | R   | 1980 | 1986 |    6 | 3/1/1980  | 12/31/1986 |
| A   | F   | R   | 1983 | 1985 |    2 | 3/1/1983  | 12/31/1985 |
| A   | F   | D   | 1983 | 1995 |   12 | 9/14/1983 | 12/31/1995 |
| A   | M   | D   | 1984 | 1987 |    3 | 3/1/1984  | 12/31/1987 |
| A   | M   | U   | 1985 | 1990 |    5 | 1/2/1985  | 12/31/1990 |
| A   | F   | D   | 1986 | 1989 |    3 | 3/1/1986  | 12/31/1989 |
| A   | M   | R   | 1986 | 1992 |    6 | 4/1986    | 12/31/1992 |
| A   | F   | D   | 1987 | 1993 |    6 | 12/1/1987 | 12/31/1993 |
| A   | F   | D   | 1989 | 1991 |    2 | 12/4/1989 | 12/31/1991 |
| A   | F   | R   | 1991 | 1996 |    5 | 1/8/1991  | 12/31/1996 |
| A   | M   | I   | 1992 | 1996 |    4 | 4/1992    | 12/31/1996 |
| A   | M   | R   | 1992 | 1998 |    6 | 1/1992    | 12/31/1998 |
| A   | M   | I   | 1993 | 2007 |   14 | 8/1993    | 12/31/2007 |
| A   | M   | D   | 1995 | 2001 |    6 | 3/1995    | 12/31/2001 |
| A   | M   | U   | 1996 | 1997 |    1 | 3/1/1996  | 12/31/1997 |
| A   | M   | R   | 1997 | 2002 |    5 | 2/1997    | 12/31/2002 |
| A   | M   | I   | 1997 | 2004 |    7 | 8/19/1997 | 12/31/2004 |
| A   | M   | R   | 1998 | 2008 |   10 | 1/6/1998  | 12/31/2008 |
| A   | F   | D   | 2001 | 2013 |   12 | 5/16/2001 | 3/3/2013   |
| A   | F   | D   | 2002 | 2003 |    1 | 11/8/2002 | 12/31/2003 |
| A   | M   | U   | 2003 | 2007 |    4 | 9/2003    | 12/31/2007 |
| A   | M   | D   | 2004 | 2011 |    7 | 9/2004    | 3/2011     |
| A   | M   | R   | 2007 | 2015 |    8 | 7/10/2007 | 42009      |
| A   | F   | R   | 2008 | 2016 |    8 | 8/1/2008  | 42373      |
| A   | M   | R   | 2008 | 2014 |    6 | 2/7/2008  | 41645      |
| A   | F   | D   | 2012 | 2017 |    5 | 7/2/2012  | 42737      |
| A   | F   | I   | 2013 | 2019 |    6 | 3/4/2013  | 43466      |
| A   | M   | D   | 2014 | 2020 |    6 | 41671     | 43836      |
| A   | M   | U   | 2015 | 9999 | 7984 | 42036     | 9999       |
| A   | M   | U   | 2016 | 9999 | 7983 | 42370     | 9999       |
| A   | F   | D   | 2017 | 9999 | 7982 | 42736     | 9999       |
| A   | F   | D   | 2019 | 9999 | 7980 | 43577     | 9999       |



label: O=N-M
labeled_formulas: O=N-M
output: {"Arithmetic-Relationship": ["O=N-M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_1826___xlsx_4304adc1f2a6771e514c6b32fa59925049640cfe.xlsx___line_167