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   | 1879 | 1889 |   10 | 3/1/1879   | 12/31/1889 |
| A   | M   | U   | 1883 | 1883 |    0 | 3/1/1883   | 12/31/1883 |
| A   | M   | U   | 1883 | 1884 |    1 | 3/1/1883   | 12/31/1884 |
| A   | M   | U   | 1884 | 1894 |   10 | 3/1/1884   | 12/31/1894 |
| A   | M   | U   | 1885 | 1892 |    7 | 3/1/1885   | 12/31/1892 |
| A   | M   | U   | 1891 | 1898 |    7 | 3/1/1891   | 12/31/1898 |
| A   | M   | U   | 1893 | 1894 |    1 | 3/1/1893   | 12/31/1894 |
| A   | M   | U   | 1895 | 1900 |    5 | 3/1/1895   | 12/31/1900 |
| A   | M   | U   | 1895 | 1902 |    7 | 3/1/1895   | 12/31/1902 |
| A   | M   | U   | 1899 | 1904 |    5 | 3/1/1899   | 12/31/1904 |
| A   | M   | U   | 1901 | 1906 |    5 | 3/1/1901   | 12/31/1906 |
| A   | M   | U   | 1903 | 1914 |   11 | 3/1/1903   | 12/31/1914 |
| A   | M   | U   | 1905 | 1910 |    5 | 3/1/1905   | 12/31/1910 |
| A   | M   | U   | 1907 | 1909 |    2 | 3/1/1907   | 12/31/1909 |
| A   | M   | U   | 1910 | 1918 |    8 | 3/1/1910   | 12/31/1918 |
| A   | M   | U   | 1911 | 1916 |    5 | 3/1/1911   | 12/31/1916 |
| A   | M   | U   | 1915 | 1926 |   11 | 3/1/1915   | 12/31/1926 |
| A   | M   | U   | 1917 | 1922 |    5 | 3/1/1917   | 12/31/1922 |
| A   | M   | U   | 1919 | 1924 |    5 | 3/1/1919   | 12/31/1924 |
| E   | M   | U   | 1922 | 1925 |    3 | 3/1/1922   | 12/31/1925 |
| E   | M   | U   | 1922 | 1926 |    4 | 3/1/1922   | 12/31/1926 |
| E   | M   | U   | 1922 | 1933 |   11 | 3/1/1922   | 12/31/1933 |
| E   | M   | U   | 1922 | 1951 |   29 | 3/1/1922   | 12/31/1951 |
| E   | M   | U   | 1923 | 1926 |    3 | 3/1/1923   | 12/31/1926 |
| E   | M   | U   | 1924 | 1935 |   11 | 3/1/1924   | 12/31/1935 |
| E   | M   | U   | 1925 | 1933 |    8 | 3/1/1925   | 12/31/1933 |
| E   | M   | U   | 1927 | 1927 |    0 | 3/1/1927   | 12/31/1927 |
| E   | M   | U   | 1927 | 1930 |    3 | 3/1/1927   | 12/31/1930 |
| E   | M   | U   | 1927 | 1934 |    7 | 3/1/1927   | 12/31/1934 |
| E   | M   | U   | 1928 | 1934 |    6 | 3/1/1928   | 12/31/1934 |
| E   | M   | U   | 1931 | 1939 |    8 | 3/1/1931   | 12/31/1939 |
| E   | M   | U   | 1934 | 1943 |    9 | 3/1/1934   | 12/31/1943 |
| E   | M   | U   | 1934 | 1946 |   12 | 3/1/1934   | 12/31/1946 |
| E   | M   | U   | 1935 | 1944 |    9 | 3/1/1935   | 12/31/1944 |
| E   | M   | U   | 1935 | 1952 |   17 | 3/1/1935   | 12/31/1952 |
| E   | M   | U   | 1936 | 1941 |    5 | 1/1/1936   | 12/31/1941 |
| E   | F   | U   | 1939 | 1939 |    0 | 1/1/1939   | 12/31/1939 |
| E   | M   | U   | 1939 | 1952 |   13 | 1/1/1939   | 12/31/1952 |
| E   | M   | U   | 1942 | 1962 |   20 | 1/1/1942   | 12/31/1962 |
| E   | M   | U   | 1944 | 1946 |    2 | 1/1/1944   | 12/31/1946 |
| E   | M   | U   | 1945 | 1971 |   26 | 1/1/1945   | 12/31/1971 |
| E   | M   | U   | 1946 | 1946 |    0 | 1/1/1946   | 12/31/1946 |
| E   | M   | U   | 1947 | 1954 |    7 | 1/1/1947   | 12/31/1954 |
| E   | M   | U   | 1948 | 1967 |   19 | 1/1/1948   | 12/31/1967 |
| E   | M   | U   | 1952 | 1971 |   19 | 1/1/1952   | 12/31/1971 |
| E   | M   | U   | 1953 | 1963 |   10 | 1/1/1953   | 12/31/1963 |
| E   | M   | D   | 1953 | 1982 |   29 | 1/1/1953   | 12/31/1982 |
| E   | M   | U   | 1962 | 1972 |   10 | 1/1/1962   | 12/31/1972 |
| E   | M   | D   | 1963 | 1998 |   35 | 1/23/1963  | 6/30/1998  |
| E   | M   | U   | 1968 | 1969 |    1 | 1/1/1968   | 12/31/1969 |
| E   | M   | D   | 1969 | 1992 |   23 | 7/8/1969   | 12/31/1992 |
| E   | M   | D   | 1970 | 1978 |    8 | 1/1/1970   | 12/31/1978 |
| E   | M   | D   | 1971 | 1977 |    6 | 1/1/1971   | 12/31/1977 |
| E   | M   | D   | 1971 | 1994 |   23 | 7/1/1971   | 12/31/1994 |
| E   | M   | U   | 1973 | 1973 |    0 | 1/1/1973   | 12/31/1973 |
| E   | M   | D   | 1973 | 1998 |   25 | 7/1/1973   | 6/30/1998  |
| E   | M   | D   | 1977 | 1980 |    3 | 1/1/1977   | 12/31/1980 |
| E   | M   | D   | 1978 | 1980 |    2 | 1/1/1978   | 12/31/1980 |
| E   | F   | D   | 1980 | 1990 |   10 | 8/29/1980  | 12/31/1990 |
| E   | F   | D   | 1980 | 1993 |   13 | 7/1/1980   | 12/31/1993 |
| E   | M   | D   | 1982 | 1998 |   16 | 7/1/1982   | 6/30/1998  |
| E   | M   | U   | 1990 | 1991 |    1 | 1/1/1990   | 12/31/1991 |
| E   | M   | R   | 1991 | 1998 |    7 | 3/20/1991  | 12/31/1998 |
| E   | M   | R   | 1993 | 1994 |    1 | 7/1/1993   | 6/30/1994  |
| E   | M   | U   | 1994 | 1999 |    5 | 7/1994     | 6/30/1999  |
| E   | M   | R   | 1994 | 2002 |    8 | 7/1994     | 6/30/2002  |
| E   | M   | D   | 1994 | 2004 |   10 | 7/1/1994   | 3/31/2004  |
| E   | F   | U   | 1998 | 2009 |   11 | 7/1/1998   | 7/31/2009  |
| E   | M   | U   | 1998 | 2004 |    6 | 7/1/1998   | 3/31/2004  |
| E   | M   | U   | 1998 | 2008 |   10 | 7/1/1998   | 12/31/2008 |
| E   | M   | U   | 1998 | 2013 |   15 | 7/1/1998   | 6/30/2013  |
| E   | M   | U   | 1999 | 2000 |    1 | 7/2/1999   | 2/29/2000  |
| E   | M   | U   | 2000 | 2004 |    4 | 2/2000     | 3/31/2004  |
| E   | M   | U   | 2002 | 2004 |    2 | 7/1/2002   | 3/31/2004  |
| E   | F   | U   | 2004 | 2018 |   14 | 3/1/2004   | 43281      |
| E   | M   | U   | 2004 | 2013 |    9 | 3/3/2004   | 5/31/2013  |
| E   | M   | U   | 2004 | 9999 | 7995 | 3/1/2004   | 9999       |
| E   | M   | U   | 2004 | 9999 | 7995 | 3/4/2004   | 9999       |
| E   | M   | U   | 2008 | 9999 | 7991 | 7/1/2008   | 9999       |
| E   | F   | U   | 2010 | 2017 |    7 | 6/1/2010   | 43009      |
| E   | M   | U   | 2013 | 9999 | 7986 | 7/1/2013   | 9999       |
| E   | M   | U   | 2013 | 2014 |    1 | 11/18/2013 | 41820      |
| E   | M   | U   | 2014 | 2019 |    5 | 41821      | 43466      |
| E   | M   | U   | 2017 | 2018 |    1 | 43040      | 43281      |
| E   | M   | U   | 2018 | 9999 | 7981 | 43101      | 9999       |
| E   | M   | U   | 2018 | 9999 | 7981 | 43101      | 9999       |
| E   | F   | U   | 2019 | 9999 | 7980 | 43515      | 9999       |



label: O=N-M
labeled_formulas: O=N-M
output: {"Arithmetic-Relationship": ["O=N-M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_1834___xlsx_4304adc1f2a6771e514c6b32fa59925049640cfe.xlsx___line_167