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   | 1896 | 1902 |    6 | 3/1/1896   | 12/31/1902 |
| A   | M   | U   | 1903 | 1906 |    3 | 3/1/1903   | 12/31/1906 |
| A   | M   | U   | 1907 | 1907 |    0 | 3/1/1907   | 12/31/1907 |
| A   | M   | U   | 1908 | 1910 |    2 | 3/1/1908   | 12/31/1910 |
| A   | M   | U   | 1908 | 1911 |    3 | 3/1/1908   | 12/31/1911 |
| A   | M   | U   | 1908 | 1912 |    4 | 3/1/1908   | 12/31/1912 |
| A   | M   | U   | 1911 | 1912 |    1 | 3/1/1911   | 12/31/1912 |
| A   | M   | U   | 1912 | 1912 |    0 | 3/1/1912   | 12/31/1912 |
| A   | M   | U   | 1917 | 1931 |   14 | 3/1/1917   | 12/31/1931 |
| A   | M   | U   | 1923 | 1930 |    7 | 3/1/1923   | 12/31/1930 |
| A   | M   | U   | 1925 | 1925 |    0 | 3/1/1925   | 12/31/1925 |
| A   | M   | U   | 1925 | 1925 |    0 | 3/1/1925   | 12/31/1925 |
| A   | M   | U   | 1925 | 1925 |    0 | 3/1/1925   | 12/31/1925 |
| A   | M   | U   | 1925 | 1926 |    1 | 3/1/1925   | 12/31/1926 |
| A   | M   | U   | 1925 | 1926 |    1 | 3/1/1925   | 12/31/1926 |
| A   | M   | U   | 1926 | 1926 |    0 | 3/1/1926   | 12/31/1926 |
| A   | M   | U   | 1927 | 1927 |    0 | 3/1/1927   | 12/31/1927 |
| A   | M   | U   | 1928 | 1928 |    0 | 3/1/1928   | 12/31/1928 |
| A   | M   | U   | 1931 | 1933 |    2 | 3/1/1931   | 12/31/1933 |
| A   | M   | U   | 1933 | 1936 |    3 | 3/1/1933   | 12/31/1936 |
| A   | M   | U   | 1934 | 1936 |    2 | 3/1/1934   | 12/31/1936 |
| A   | M   | U   | 1936 | 1936 |    0 | 3/1/1936   | 12/31/1936 |
| A   | M   | U   | 1936 | 1936 |    0 | 3/1/1936   | 12/31/1936 |
| A   | M   | U   | 1936 | 1936 |    0 | 3/1/1936   | 12/31/1936 |
| A   | M   | U   | 1936 | 1936 |    0 | 3/1/1936   | 12/31/1936 |
| A   | M   | U   | 1936 | 1945 |    9 | 3/1/1936   | 12/31/1945 |
| A   | M   | U   | 1937 | 1937 |    0 | 3/1/1937   | 12/31/1937 |
| A   | M   | U   | 1937 | 1938 |    1 | 3/1/1937   | 12/31/1938 |
| A   | M   | U   | 1937 | 1939 |    2 | 3/1/1937   | 12/31/1939 |
| A   | M   | U   | 1937 | 1943 |    6 | 3/1/1937   | 12/31/1943 |
| A   | M   | U   | 1938 | 1938 |    0 | 3/1/1938   | 12/31/1938 |
| A   | M   | U   | 1938 | 1939 |    1 | 3/1/1938   | 12/31/1939 |
| A   | M   | U   | 1939 | 1945 |    6 | 3/1/1939   | 12/31/1945 |
| A   | M   | U   | 1939 | 1951 |   12 | 3/1/1939   | 12/31/1951 |
| A   | M   | U   | 1940 | 1952 |   12 | 3/1/1940   | 12/31/1952 |
| A   | M   | U   | 1943 | 1959 |   16 | 3/1/1943   | 12/31/1959 |
| A   | M   | U   | 1945 | 1952 |    7 | 3/1/1945   | 12/31/1952 |
| A   | M   | U   | 1947 | 1959 |   12 | 3/1/1947   | 12/31/1959 |
| A   | M   | U   | 1952 | 1961 |    9 | 3/1/1952   | 12/31/1961 |
| A   | M   | U   | 1953 | 1955 |    2 | 3/1/1953   | 12/31/1955 |
| A   | M   | U   | 1953 | 1967 |   14 | 3/1/1953   | 12/31/1967 |
| A   | M   | U   | 1956 | 1965 |    9 | 3/1/1956   | 12/31/1965 |
| A   | M   | U   | 1960 | 1963 |    3 | 3/1/1960   | 12/31/1963 |
| A   | M   | U   | 1960 | 1971 |   11 | 3/1/1960   | 12/31/1971 |
| A   | M   | U   | 1961 | 1967 |    6 | 3/1/1961   | 12/31/1967 |
| A   | M   | U   | 1963 | 1968 |    5 | 3/1/1963   | 12/31/1968 |
| A   | M   | R   | 1965 | 1975 |   10 | 3/1/1965   | 12/31/1975 |
| A   | M   | R   | 1967 | 1977 |   10 | 3/1/1967   | 12/31/1977 |
| A   | M   | U   | 1968 | 1970 |    2 | 3/1/1968   | 12/31/1970 |
| A   | M   | U   | 1968 | 1973 |    5 | 3/1/1968   | 12/31/1973 |
| A   | M   | R   | 1970 | 1979 |    9 | 3/1/1970   | 12/31/1979 |
| A   | M   | D   | 1971 | 1979 |    8 | 3/1/1971   | 12/31/1979 |
| A   | M   | U   | 1973 | 1973 |    0 | 3/1/1973   | 12/31/1973 |
| A   | F   | D   | 1975 | 1979 |    4 | 3/1/1975   | 12/31/1979 |
| A   | M   | D   | 1975 | 1985 |   10 | 3/1/1975   | 12/31/1985 |
| A   | M   | D   | 1978 | 1980 |    2 | 3/1/1978   | 12/31/1980 |
| A   | F   | R   | 1979 | 1983 |    4 | 3/1/1979   | 12/31/1983 |
| A   | F   | R   | 1979 | 1988 |    9 | 3/1/1979   | 12/31/1988 |
| A   | M   | D   | 1979 | 1985 |    6 | 3/1/1979   | 12/31/1985 |
| A   | M   | R   | 1981 | 1983 |    2 | 3/1/1981   | 12/31/1983 |
| A   | M   | D   | 1984 | 1990 |    6 | 5/7/1984   | 10/1990    |
| A   | M   | R   | 1984 | 1991 |    7 | 5/7/1984   | 12/31/1991 |
| A   | M   | D   | 1987 | 1992 |    5 | 7/14/1987  | 12/31/1992 |
| A   | M   | D   | 1988 | 1995 |    7 | 5/25/1988  | 4/1995     |
| A   | M   | D   | 1989 | 1999 |   10 | 12/1989    | 10/1999    |
| A   | M   | D   | 1990 | 1993 |    3 | 11/1990    | 12/31/1993 |
| A   | F   | D   | 1993 | 1997 |    4 | 6/1993     | 3/1997     |
| A   | M   | D   | 1993 | 1998 |    5 | 4/1993     | 5/1998     |
| A   | M   | R   | 1993 | 2001 |    8 | 4/1/1993   | 12/31/2001 |
| A   | M   | R   | 1995 | 2001 |    6 | 5/8/1995   | 12/31/2001 |
| A   | F   | R   | 1997 | 2001 |    4 | 4/30/1997  | 12/31/2001 |
| A   | M   | R   | 1998 | 2003 |    5 | 6/3/1998   | 8/2003     |
| A   | M   | R   | 1999 | 2007 |    8 | 11/10/1999 | 5/2007     |
| A   | M   | R   | 2001 | 2005 |    4 | 6/25/2001  | 12/31/2005 |
| A   | F   | R   | 2002 | 2010 |    8 | 2/6/2002   | 5/2010     |
| A   | M   | D   | 2003 | 2008 |    5 | 9/2003     | 12/31/2008 |
| A   | M   | D   | 2005 | 2006 |    1 | 6/2005     | 12/31/2006 |
| A   | M   | D   | 2005 | 2015 |   10 | 6/1/2005   | 42094      |
| A   | M   | D   | 2007 | 2011 |    4 | 6/27/2007  | 5/2011     |
| A   | M   | D   | 2008 | 2013 |    5 | 6/30/2008  | 4/1/2013   |
| A   | M   | D   | 2008 | 2017 |    9 | 6/30/2008  | 43009      |
| A   | M   | R   | 2010 | 9999 | 7989 | 6/15/2010  | 9999       |
| A   | F   | U   | 2011 | 2016 |    5 | 6/30/2011  | 42461      |
| A   | F   | D   | 2013 | 9999 | 7986 | 10/2/2013  | 9999       |
| A   | M   | U   | 2015 | 9999 | 7984 | 42248      | 9999       |
| A   | M   | D   | 2016 | 9999 | 7983 | 42522      | 9999       |
| A   | M   | U   | 2017 | 2019 |    2 | 43040      | 43678      |
| A   | M   | U   | 2019 | 9999 | 7980 | 43700      | 9999       |



label: O=N-M
labeled_formulas: O=N-M
output: {"Arithmetic-Relationship": ["O=N-M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_1833___xlsx_4304adc1f2a6771e514c6b32fa59925049640cfe.xlsx___line_167