Please read the following table in Markdown format and then answer the question according to the table. Table cells in one row are seperated by '|', and different rows are seperated by '
'.

Table:
| Institution | Location | Nickname | Founded | Historical Affiliation | Enrollment | Primary Conference |
| --- | --- | --- | --- | --- | --- | --- |
| Brown University | Providence, Rhode Island | Bears | 1764 | Nonsectarian, founded by Baptists, but founding charter promises "no religious tests" and "full liberty of conscience" | 7,744 | Ivy League |
| Clarkson University | Potsdam, New York | Golden Knights | 1896 | Private/Non-sectarian | 3,100 | Liberty League (D-III) |
| Colgate University | Hamilton, New York | Raiders | 1819 | Private/Non-sectarian, founded by Baptists | 2,800 | Patriot League |
| Cornell University | Ithaca, New York | Big Red | 1865 | Private/Non-sectarian | 20,400 | Ivy League |
| Dartmouth College | Hanover, New Hampshire | Big Green | 1769 | Private/Congregationalist | 5,753 | Ivy League |
| Harvard University | Cambridge, Massachusetts | Crimson | 1636 | Private/Unitarian | 20,042 | Ivy League |
| Princeton University | Princeton, New Jersey | Tigers | 1746 | Nonsectarian, but founded by Presbyterians | 6,677 | Ivy League |
| Quinnipiac University | Hamden, Connecticut | Bobcats | 1929 | Private/Non-sectarian | 7,700 | MAAC |
| Rensselaer Polytechnic Institute | Troy, New York | Engineers | 1824 | Private/Non-sectarian | 6,376 | Liberty League (D-III) |
| St. Lawrence University | Canton, New York | Saints | 1856 | Non-denominational, founded by Universalist Church of America | 2,100 | Liberty League (D-III) |
| Union College | Schenectady, New York | Dutchmen | 1795 | Private/Non-sectarian | 2,100 | Liberty League (D-III) |
| Yale University | New Haven, Connecticut | Bulldogs | 1701 | Private/Congregationalist | 11,483 | Ivy League |
Question:
how many institutions have a private historical affiliation?
Answer:
9