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   | 1867 | 1871 |    4 | 3/1/1867   | 12/31/1871 |
| A   | M   | U   | 1871 | 1872 |    1 | 3/1/1871   | 12/31/1872 |
| A   | M   | U   | 1872 | 1874 |    2 | 3/1/1872   | 12/31/1874 |
| A   | M   | U   | 1874 | 1876 |    2 | 3/1/1874   | 12/31/1876 |
| A   | M   | U   | 1876 | 1878 |    2 | 3/1/1876   | 12/31/1878 |
| A   | M   | U   | 1878 | 1880 |    2 | 3/1/1878   | 12/31/1880 |
| A   | M   | U   | 1880 | 1881 |    1 | 3/1/1880   | 12/31/1881 |
| A   | M   | U   | 1881 | 1885 |    4 | 3/1/1881   | 12/31/1885 |
| A   | M   | U   | 1885 | 1887 |    2 | 3/1/1885   | 12/31/1887 |
| A   | M   | U   | 1887 | 1890 |    3 | 3/1/1887   | 12/31/1890 |
| A   | M   | U   | 1890 | 1892 |    2 | 3/1/1890   | 12/31/1892 |
| A   | M   | U   | 1891 | 1897 |    6 | 3/1/1891   | 12/31/1897 |
| A   | M   | U   | 1897 | 1900 |    3 | 3/1/1897   | 12/31/1900 |
| A   | M   | U   | 1901 | 1909 |    8 | 3/1/1901   | 12/31/1909 |
| A   | M   | U   | 1906 | 1913 |    7 | 3/1/1906   | 12/31/1913 |
| A   | M   | U   | 1906 | 1915 |    9 | 3/1/1906   | 12/31/1915 |
| A   | M   | U   | 1909 | 1913 |    4 | 3/1/1909   | 12/31/1913 |
| A   | M   | U   | 1913 | 1915 |    2 | 3/1/1913   | 12/31/1915 |
| A   | M   | U   | 1913 | 1917 |    4 | 3/1/1913   | 12/31/1917 |
| A   | M   | U   | 1915 | 1917 |    2 | 3/1/1915   | 12/31/1917 |
| A   | M   | U   | 1915 | 1917 |    2 | 3/1/1915   | 12/31/1917 |
| A   | M   | U   | 1915 | 1921 |    6 | 3/1/1915   | 12/31/1921 |
| A   | M   | U   | 1917 | 1921 |    4 | 3/1/1917   | 12/31/1921 |
| A   | M   | U   | 1921 | 1922 |    1 | 3/1/1921   | 12/31/1922 |
| A   | M   | U   | 1921 | 1927 |    6 | 3/1/1921   | 12/31/1927 |
| A   | M   | U   | 1922 | 1927 |    5 | 3/1/1922   | 12/31/1927 |
| A   | M   | U   | 1927 | 1929 |    2 | 3/1/1927   | 12/31/1929 |
| A   | M   | U   | 1927 | 1931 |    4 | 3/1/1927   | 12/31/1931 |
| A   | M   | U   | 1928 | 1933 |    5 | 3/1/1928   | 12/31/1933 |
| A   | M   | U   | 1929 | 1933 |    4 | 3/1/1929   | 12/31/1933 |
| A   | M   | U   | 1929 | 1933 |    4 | 3/1/1929   | 12/31/1933 |
| A   | M   | U   | 1931 | 1933 |    2 | 3/1/1931   | 12/31/1933 |
| A   | M   | U   | 1932 | 1938 |    6 | 3/1/1932   | 12/31/1938 |
| A   | M   | U   | 1935 | 1941 |    6 | 3/1/1935   | 12/31/1941 |
| A   | M   | U   | 1935 | 1942 |    7 | 3/1/1935   | 12/31/1942 |
| A   | M   | U   | 1939 | 1945 |    6 | 3/1/1939   | 12/31/1945 |
| A   | M   | U   | 1941 | 1949 |    8 | 3/1/1941   | 12/31/1949 |
| A   | M   | U   | 1943 | 1949 |    6 | 3/1/1943   | 12/31/1949 |
| A   | M   | U   | 1951 | 1951 |    0 | 3/1/1951   | 12/31/1951 |
| A   | M   | U   | 1951 | 1954 |    3 | 3/1/1951   | 12/31/1954 |
| A   | M   | U   | 1951 | 1957 |    6 | 3/1/1951   | 12/31/1957 |
| A   | M   | U   | 1951 | 1959 |    8 | 3/1/1951   | 12/31/1959 |
| A   | M   | U   | 1955 | 1960 |    5 | 3/1/1955   | 12/31/1960 |
| A   | M   | U   | 1957 | 1962 |    5 | 3/1/1957   | 12/31/1962 |
| A   | M   | U   | 1959 | 1960 |    1 | 3/1/1959   | 12/31/1960 |
| A   | F   | U   | 1960 | 1963 |    3 | 3/1/1960   | 12/31/1963 |
| A   | M   | U   | 1962 | 1963 |    1 | 3/1/1962   | 12/31/1963 |
| A   | M   | U   | 1962 | 1963 |    1 | 3/1/1962   | 12/31/1963 |
| A   | M   | U   | 1963 | 1963 |    0 | 3/1/1963   | 12/31/1963 |
| A   | M   | U   | 1963 | 1965 |    2 | 3/1/1963   | 12/31/1965 |
| A   | M   | U   | 1963 | 1971 |    8 | 3/1/1963   | 12/31/1971 |
| A   | M   | R   | 1963 | 1975 |   12 | 3/1/1963   | 12/31/1975 |
| A   | M   | U   | 1965 | 1967 |    2 | 3/1/1965   | 12/31/1967 |
| A   | M   | U   | 1967 | 1973 |    6 | 3/1/1967   | 12/31/1973 |
| A   | M   | U   | 1971 | 1973 |    2 | 3/1/1971   | 12/31/1973 |
| A   | F   | D   | 1973 | 1977 |    4 | 3/1/1973   | 12/31/1977 |
| A   | M   | D   | 1973 | 1975 |    2 | 3/1/1973   | 12/31/1975 |
| A   | M   | D   | 1975 | 1978 |    3 | 3/1/1975   | 12/31/1978 |
| A   | M   | R   | 1975 | 1980 |    5 | 3/1/1975   | 12/31/1980 |
| A   | M   | R   | 1977 | 1981 |    4 | 3/1/1977   | 12/31/1981 |
| A   | M   | D   | 1978 | 1978 |    0 | 3/1/1978   | 12/31/1978 |
| A   | M   | D   | 1979 | 1984 |    5 | 3/1/1979   | 12/31/1984 |
| A   | M   | R   | 1980 | 1983 |    3 | 3/1/1980   | 12/31/1983 |
| A   | M   | R   | 1981 | 1983 |    2 | 3/1/1981   | 12/31/1983 |
| A   | M   | R   | 1981 | 1983 |    2 | 3/1/1981   | 12/31/1983 |
| A   | F   | R   | 1983 | 1990 |    7 | 7/20/1983  | 3/1990     |
| A   | M   | D   | 1983 | 1987 |    4 | 3/1/1983   | 12/31/1987 |
| A   | M   | I   | 1983 | 1989 |    6 | 3/1/1983   | 12/31/1989 |
| A   | M   | D   | 1983 | 1993 |   10 | 4/11/1983  | 3/1993     |
| A   | M   | D   | 1985 | 1989 |    4 | 3/1/1985   | 12/31/1989 |
| A   | M   | U   | 1988 | 1988 |    0 | 3/1/1988   | 12/31/1988 |
| A   | M   | D   | 1988 | 1991 |    3 | 5/2/1988   | 3/1991     |
| A   | F   | D   | 1989 | 1999 |   10 | 4/24/1989  | 3/1999     |
| A   | M   | R   | 1989 | 1997 |    8 | 10/13/1989 | 3/1997     |
| A   | M   | I   | 1990 | 1995 |    5 | 4/11/1990  | 3/1995     |
| A   | M   | I   | 1991 | 2001 |   10 | 4/11/1991  | 1/2001     |
| A   | M   | R   | 1993 | 1998 |    5 | 4/1993     | 3/1998     |
| A   | F   | R   | 1995 | 2010 |   15 | 4/12/1995  | 3/2010     |
| A   | F   | R   | 1997 | 2007 |   10 | 4/11/1997  | 3/2007     |
| A   | M   | R   | 1998 | 2008 |   10 | 4/1998     | 3/2008     |
| A   | M   | I   | 1999 | 2010 |   11 | 4/11/1999  | 12/31/2010 |
| A   | M   | U   | 2001 | 2006 |    5 | 2/5/2001   | 3/2006     |
| A   | F   | I   | 2006 | 2011 |    5 | 4/1/2006   | 3/2011     |
| A   | M   | U   | 2007 | 2012 |    5 | 4/2007     | 41009      |
| A   | F   | D   | 2008 | 2012 |    4 | 4/2008     | 41274      |
| A   | M   | U   | 2010 | 2015 |    5 | 4/2010     | 42104      |
| A   | M   | U   | 2011 | 2013 |    2 | 4/11/2011  | 4/22/2013  |
| A   | M   | R   | 2011 | 2014 |    3 | 3/2011     | 41739      |
| A   | M   | R   | 2012 | 2017 |    5 | 4/11/2012  | 42835      |
| A   | F   | U   | 2013 | 9999 | 7986 | 3/1/2013   | 9999       |
| A   | M   | U   | 2013 | 2019 |    6 | 6/1/2013   | 43525      |
| A   | M   | R   | 2014 | 2019 |    5 | 41730      | 43556      |
| A   | M   | R   | 2017 | 9999 | 7982 | 42739      | 9999       |
| A   | M   | U   | 2016 | 9999 | 7983 | 42376      | 9999       |
| A   | M   | U   | 2019 | 9999 | 7980 | 43556      | 9999       |
| A   | M   | R   | 2019 | 9999 | 7980 | 43549      | 9999       |



label: O=N-M
labeled_formulas: O=N-M
output: {"Arithmetic-Relationship": ["O=N-M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_1832___xlsx_4304adc1f2a6771e514c6b32fa59925049640cfe.xlsx___line_167