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          |
|:----|:----|:----|-----:|-----:|-----:|:----------|:-----------|
| E   | M   | U   | 1912 | 1912 |    0 | 1/1/1912  | 12/31/1912 |
| E   | M   | U   | 1912 | 1916 |    4 | 1/1/1912  | 12/31/1916 |
| E   | M   | U   | 1912 | 1918 |    6 | 1/1/1912  | 12/31/1918 |
| E   | M   | U   | 1912 | 1932 |   20 | 1/1/1912  | 12/31/1932 |
| E   | M   | U   | 1917 | 1928 |   11 | 1/1/1917  | 12/31/1928 |
| E   | M   | U   | 1919 | 1924 |    5 | 1/1/1919  | 12/31/1924 |
| E   | M   | U   | 1925 | 1925 |    0 | 1/1/1925  | 12/31/1925 |
| E   | M   | U   | 1925 | 1926 |    1 | 1/1/1925  | 12/31/1926 |
| E   | M   | U   | 1926 | 1930 |    4 | 1/1/1926  | 12/31/1930 |
| E   | M   | U   | 1929 | 1934 |    5 | 1/1/1929  | 12/31/1934 |
| E   | M   | U   | 1931 | 1932 |    1 | 1/1/1931  | 12/31/1932 |
| E   | M   | U   | 1933 | 1938 |    5 | 1/1/1933  | 12/31/1938 |
| E   | M   | U   | 1933 | 1948 |   15 | 1/1/1933  | 12/31/1948 |
| E   | M   | U   | 1935 | 1945 |   10 | 1/1/1935  | 12/31/1945 |
| E   | M   | U   | 1939 | 1943 |    4 | 1/1/1939  | 12/31/1943 |
| E   | M   | U   | 1941 | 1943 |    2 | 1/1/1941  | 12/31/1943 |
| E   | M   | U   | 1941 | 1943 |    2 | 1/1/1941  | 12/31/1943 |
| E   | M   | U   | 1941 | 1943 |    2 | 1/1/1941  | 12/31/1943 |
| E   | M   | U   | 1943 | 1944 |    1 | 1/1/1943  | 12/31/1944 |
| E   | M   | U   | 1943 | 1945 |    2 | 1/1/1943  | 12/31/1945 |
| E   | M   | U   | 1943 | 1945 |    2 | 1/1/1943  | 12/31/1945 |
| E   | M   | U   | 1943 | 1951 |    8 | 1/1/1943  | 12/31/1951 |
| E   | M   | U   | 1944 | 1945 |    1 | 1/1/1944  | 12/31/1945 |
| E   | M   | U   | 1944 | 1951 |    7 | 1/1/1944  | 12/31/1951 |
| E   | M   | U   | 1945 | 1947 |    2 | 1/1/1945  | 12/31/1947 |
| E   | M   | U   | 1945 | 1947 |    2 | 1/1/1945  | 12/31/1947 |
| E   | M   | U   | 1945 | 1947 |    2 | 1/1/1945  | 12/31/1947 |
| E   | M   | U   | 1947 | 1948 |    1 | 1/1/1947  | 12/31/1948 |
| E   | M   | U   | 1947 | 1952 |    5 | 1/1/1947  | 12/31/1952 |
| E   | M   | U   | 1948 | 1950 |    2 | 1/1/1948  | 12/31/1950 |
| E   | M   | U   | 1948 | 1951 |    3 | 1/1/1948  | 12/31/1951 |
| E   | M   | U   | 1949 | 1963 |   14 | 1/1/1949  | 12/31/1963 |
| E   | M   | U   | 1950 | 1950 |    0 | 1/1/1950  | 12/31/1950 |
| E   | M   | U   | 1950 | 1951 |    1 | 1/1/1950  | 12/31/1951 |
| E   | M   | U   | 1951 | 1952 |    1 | 1/1/1951  | 12/31/1952 |
| E   | M   | U   | 1951 | 1955 |    4 | 1/1/1951  | 12/31/1955 |
| E   | M   | U   | 1951 | 1959 |    8 | 1/1/1951  | 12/31/1959 |
| E   | M   | U   | 1951 | 1959 |    8 | 1/1/1951  | 12/31/1959 |
| E   | M   | U   | 1953 | 1959 |    6 | 1/1/1953  | 12/31/1959 |
| E   | M   | U   | 1953 | 1962 |    9 | 1/1/1953  | 12/31/1962 |
| E   | M   | U   | 1955 | 1957 |    2 | 1/1/1955  | 12/31/1957 |
| E   | M   | U   | 1957 | 1959 |    2 | 1/1/1957  | 12/31/1959 |
| E   | M   | U   | 1959 | 1961 |    2 | 1/1/1959  | 12/31/1961 |
| E   | M   | U   | 1959 | 1961 |    2 | 1/1/1959  | 12/31/1961 |
| E   | M   | U   | 1959 | 1961 |    2 | 1/1/1959  | 12/31/1961 |
| E   | M   | U   | 1959 | 1965 |    6 | 1/1/1959  | 12/31/1965 |
| E   | M   | U   | 1961 | 1963 |    2 | 1/1/1961  | 12/31/1963 |
| E   | M   | U   | 1961 | 1963 |    2 | 1/1/1961  | 12/31/1963 |
| E   | M   | U   | 1961 | 1968 |    7 | 1/1/1961  | 12/31/1968 |
| E   | M   | U   | 1963 | 1967 |    4 | 1/1/1963  | 12/31/1967 |
| E   | M   | U   | 1963 | 1967 |    4 | 1/1/1963  | 12/31/1967 |
| E   | M   | U   | 1963 | 1968 |    5 | 1/1/1963  | 12/31/1968 |
| E   | M   | D   | 1963 | 1981 |   18 | 1/1/1963  | 12/31/1981 |
| E   | M   | D   | 1965 | 1976 |   11 | 1/1/1965  | 12/31/1976 |
| E   | M   | U   | 1967 | 1968 |    1 | 1/1/1967  | 12/31/1968 |
| E   | M   | D   | 1967 | 1975 |    8 | 1/1/1967  | 12/31/1975 |
| E   | M   | U   | 1969 | 1971 |    2 | 1/1/1969  | 12/31/1971 |
| E   | M   | U   | 1969 | 1971 |    2 | 1/1/1969  | 12/31/1971 |
| E   | M   | D   | 1969 | 1974 |    5 | 1/1/1969  | 12/31/1974 |
| E   | M   | D   | 1971 | 1975 |    4 | 1/1/1971  | 12/31/1975 |
| E   | M   | D   | 1971 | 1982 |   11 | 1/1/1971  | 12/31/1982 |
| E   | F   | D   | 1975 | 1978 |    3 | 1/1/1975  | 12/31/1978 |
| E   | M   | D   | 1975 | 1975 |    0 | 1/1/1975  | 12/31/1975 |
| E   | M   | D   | 1975 | 1979 |    4 | 1/1/1975  | 12/31/1979 |
| E   | M   | D   | 1975 | 1980 |    5 | 1/1/1975  | 12/31/1980 |
| E   | M   | D   | 1976 | 1988 |   12 | 1/1/1976  | 12/31/1988 |
| E   | M   | D   | 1979 | 1983 |    4 | 1/1/1979  | 12/31/1983 |
| E   | F   | U   | 1980 | 1983 |    3 | 1/1/1980  | 12/31/1983 |
| E   | M   | R   | 1981 | 1984 |    3 | 1/1/1981  | 12/31/1984 |
| E   | M   | D   | 1981 | 1998 |   17 | 2/1/1981  | 12/31/1998 |
| E   | M   | D   | 1982 | 1984 |    2 | 1/1/1982  | 12/31/1984 |
| E   | F   | D   | 1983 | 1986 |    3 | 1/1/1983  | 12/31/1986 |
| E   | M   | D   | 1983 | 1986 |    3 | 1/1/1983  | 12/31/1986 |
| E   | M   | D   | 1984 | 1985 |    1 | 1/1/1984  | 12/31/1985 |
| E   | F   | D   | 1985 | 1986 |    1 | 1/1/1985  | 12/31/1986 |
| E   | F   | U   | 1986 | 1986 |    0 | 1/1/1986  | 12/31/1986 |
| E   | M   | U   | 1986 | 1986 |    0 | 1/1/1986  | 12/31/1986 |
| E   | M   | D   | 1987 | 1990 |    3 | 1/16/1987 | 12/31/1990 |
| E   | M   | R   | 1987 | 1991 |    4 | 1/20/1987 | 12/31/1991 |
| E   | M   | R   | 1987 | 1995 |    8 | 2/17/1987 | 12/31/1995 |
| E   | M   | D   | 1987 | 2004 |   17 | 1/1/1987  | 12/31/2004 |
| E   | M   | D   | 1989 | 1994 |    5 | 1/3/1989  | 12/31/1994 |
| E   | M   | U   | 1990 | 1991 |    1 | 1/1/1990  | 12/31/1991 |
| E   | F   | D   | 1991 | 1994 |    3 | 4/16/1991 | 12/31/1994 |
| E   | M   | D   | 1991 | 1996 |    5 | 3/18/1991 | 12/31/1996 |
| E   | F   | D   | 1995 | 1997 |    2 | 1/1995    | 12/31/1997 |
| E   | F   | R   | 1995 | 1998 |    3 | 8/1995    | 12/31/1998 |
| E   | M   | D   | 1995 | 1998 |    3 | 3/1995    | 12/31/1998 |
| E   | F   | D   | 1999 | 2006 |    7 | 1/1/1999  | 12/31/2006 |
| E   | M   | R   | 1999 | 2001 |    2 | 1/1999    | 12/31/2001 |
| E   | M   | D   | 1999 | 2002 |    3 | 1/1999    | 12/31/2002 |
| E   | M   | R   | 1999 | 2004 |    5 | 1/1/1999  | 12/31/2004 |
| E   | M   | R   | 2001 | 2002 |    1 | 5/2001    | 12/31/2002 |
| E   | F   | U   | 2003 | 2006 |    3 | 1/2003    | 12/31/2006 |
| E   | M   | U   | 2003 | 2010 |    7 | 1/2003    | 12/31/2010 |
| E   | M   | D   | 2005 | 2008 |    3 | 1/2005    | 12/31/2008 |
| E   | M   | D   | 2005 | 2012 |    7 | 1/1/2005  | 12/31/2012 |
| E   | F   | U   | 2007 | 2010 |    3 | 1/1/2007  | 6/23/2010  |
| E   | M   | D   | 2007 | 2010 |    3 | 1/1/2007  | 40330      |
| E   | M   | D   | 2009 | 2011 |    2 | 1/1/2009  | 10/7/2011  |
| E   | F   | D   | 2010 | 2014 |    4 | 7/1/2010  | 41704      |
| E   | M   | I   | 2011 | 2012 |    1 | 11/2011   | 12/31/2012 |
| E   | M   | R   | 2011 | 2018 |    7 | 1/1/2011  | 37201      |
| E   | M   | U   | 2011 | 2014 |    3 | 1/1/2011  | 42004      |
| E   | F   | D   | 2013 | 2014 |    1 | 1/1/2013  | 42004      |
| E   | F   | D   | 2013 | 9999 | 7986 | 1/1/2013  | 9999       |
| E   | F   | D   | 2015 | 2018 |    3 | 42005     | 43256      |
| E   | F   | D   | 2017 | 9999 | 7982 | 42736     | 9999       |
| E   | M   | D   | 2015 | 2018 |    3 | 42005     | 43256      |
| E   | M   | R   | 2018 | 9999 | 7981 | 43410     | 9999       |
| E   | F   | D   | 2019 | 9999 | 7980 | 43466     | 9999       |
| E   | M   | D   | 2019 | 9999 | 7980 | 43466     | 9999       |



label: O=N-M
labeled_formulas: O=N-M
output: {"Arithmetic-Relationship": ["O=N-M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_1830___xlsx_4304adc1f2a6771e514c6b32fa59925049640cfe.xlsx___line_167