Task: semantic-join (source dataset: DataXFormer)

You are given two input tables below. Your task is to identify the most likely semantic relationships between values of these two columns, and then output pairs of values from Table 1 and Table 2, that can be joined/linked based on the inferred semantic relationships. 

No explanation is needed, only return your answer in JSON format: {"output": <answer>}, where the <answer> is a list of lists. Each inner list should contain exactly one value from Table 1, and its semantically matching value from Table 2. If a value from Table 1 does not have corresponding value from Table 2, you can omit it in the answer. But be careful, not to miss any values from Table 1 that do have corresponding matching values in Table 2.

Input Table 1:
| Col_0                                   |
|:----------------------------------------|
| California Institute of Technology      |
| Harvard University                      |
| Harvey Mudd College                     |
| Dartmouth College                       |
| Stanford University                     |
| Princeton University                    |
| Yale University                         |
| University of Notre Dame                |
| University of Pennsylvania              |
| Duke University                         |
| Lehigh University                       |
| Union College                           |
| Amherst College                         |
| Worcester Polytechnic Institute         |
| University of California Berkeley       |
| Carnegie Mellon University              |
| Colgate University                      |
| Columbia University                     |
| Rensselaer Polytechnic Institute        |
| Bowdoin College                         |
| Brown University                        |
| Villanova University                    |
| Rice University                         |
| Cornell University                      |
| Lafayette College                       |
| Stevens Institute of Technology         |
| Georgia Institute of Technology         |
| Santa Clara University                  |
| College of the Holy Cross               |
| University of Chicago                   |
| Manhattan College                       |
| University of Virginia                  |
| Williams College                        |
| Rose-Hulman Institute of Technology     |
| Tufts University                        |
| Washington and Lee University           |
| Bucknell University                     |
| University of California San Diego      |
| University of California at Los Angeles |
| University of Southern California       |

Input Table 2:
| Col_1          |
|:---------------|
| California     |
| Massachusetts  |
| California     |
| New Hampshire  |
| California     |
| New Jersey     |
| Connecticut    |
| Indiana        |
| Pennsylvania   |
| North Carolina |
| Pennsylvania   |
| New York       |
| Massachusetts  |
| Massachusetts  |
| California     |
| Pennsylvania   |
| New York       |
| New York       |
| New York       |
| Maine          |
| Massachusetts  |
| Pennsylvania   |
| Texas          |
| New Jersey     |
| Indiana        |
| New Jersey     |
| Georgia        |
| California     |
| Massachusetts  |
| Illinois       |
| New York       |
| Virginia       |
| Massachusetts  |
| Indiana        |
| Massachusetts  |
| Virginia       |
| Pennsylvania   |
| California     |
| California     |
| California     |

Joined Table:



label: California Institute of Technology
California
Harvard University
Massachusetts
Harvey Mudd College
California
Dartmouth College
New Hampshire
Stanford University
California
Princeton University
New Jersey
Yale University
Connecticut
University of Notre Dame
Indiana
University of Pennsylvania
Pennsylvania
Duke University
North Carolina
Lehigh University
Pennsylvania
Union College
New York
Amherst College
Massachusetts
Worcester Polytechnic Institute
Massachusetts
University of California Berkeley
California
Carnegie Mellon University
Pennsylvania
Colgate University
New York
Columbia University
New York
Rensselaer Polytechnic Institute
New York
Bowdoin College
Maine
Brown University
Massachusetts
Villanova University
Pennsylvania
Rice University
Texas
Cornell University
New Jersey
Lafayette College
Indiana
Stevens Institute of Technology
New Jersey
Georgia Institute of Technology
Georgia
Santa Clara University
California
College of the Holy Cross
Massachusetts
University of Chicago
Illinois
Manhattan College
New York
University of Virginia
Virginia
Williams College
Massachusetts
Rose-Hulman Institute of Technology
Indiana
Tufts University
Massachusetts
Washington and Lee University
Virginia
Bucknell University
Pennsylvania
University of California San Diego
California
University of California at Los Angeles
California
University of Southern California
California