Task: semantic-join (source dataset: SEMA-join)

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                  |
|:-----------------------|
| William Henry Harrison |
| Martin Van Buren       |
| John Adams             |
| George Washington      |
| Zachary Taylor         |
| Richard Nixon          |
| John Quincy Adams      |
| Dwight D. Eisenhower   |
| Herbert Hoover         |
| James A. Garfield      |
| Bill Clinton           |
| John F. Kennedy        |
| George W. Bush         |
| Franklin D. Roosevelt  |
| Jimmy Carter           |
| Thomas Jefferson       |
| James K. Polk          |
| James Madison          |
| Andrew Johnson         |
| Ulysses S. Grant       |
| John Tyler             |
| Andrew Jackson         |
| William Howard Taft    |
| Ronald Reagan          |
| Woodrow Wilson         |
| Grover Cleveland       |
| James Buchanan         |
| Chester A. Arthur      |
| Warren G. Harding      |
| Gerald Ford            |
| Benjamin Harrison      |
| Franklin Pierce        |
| Abraham Lincoln        |
| Calvin Coolidge        |
| Millard Fillmore       |
| Rutherford B. Hayes    |
| Barack Obama           |
| James Monroe           |
| Harry S. Truman        |
| George H. W. Bush      |
| William McKinley       |
| Theodore Roosevelt     |
| Lyndon B. Johnson      |

Input Table 2:
| Col_1          |
|:---------------|
| Vermont        |
| North Carolina |
| New York       |
| Kentucky       |
| Hawaii         |
| California     |
| Arkansas       |
| New Jersey     |
| South Carolina |
| Pennsylvania   |
| Nebraska       |
| Iowa           |
| Massachusetts  |
| Texas          |
| Illinois       |
| New Hampshire  |
| Missouri       |
| Connecticut    |
| Ohio           |
| Georgia        |
| Virginia       |

Joined Table:



label: Zachary Taylor
Virginia
Warren G. Harding
Ohio
John Quincy Adams
Massachusetts
John F. Kennedy
Massachusetts
Grover Cleveland
New Jersey
William Henry Harrison
Virginia
John Tyler
Virginia
William Howard Taft
Ohio
James Buchanan
Pennsylvania
Rutherford B. Hayes
Ohio
Dwight D. Eisenhower
Texas
Chester A. Arthur
Vermont
Franklin Pierce
New Hampshire
Barack Obama
Hawaii
Bill Clinton
Arkansas
Franklin D. Roosevelt
New York
Martin Van Buren
New York
Harry S. Truman
Missouri
Andrew Jackson
South Carolina
George H. W. Bush
Massachusetts
James A. Garfield
Ohio
George W. Bush
Connecticut
Theodore Roosevelt
New York
William McKinley
Ohio
Abraham Lincoln
Kentucky
Benjamin Harrison
Ohio
Gerald Ford
Nebraska
James K. Polk
North Carolina
Jimmy Carter
Georgia
Calvin Coolidge
Vermont
Ulysses S. Grant
Ohio
James Madison
Virginia
John Adams
Massachusetts
Andrew Johnson
North Carolina
Thomas Jefferson
Virginia
Lyndon B. Johnson
Texas
Woodrow Wilson
Virginia
Millard Fillmore
New York
Ronald Reagan
Illinois
Herbert Hoover
Iowa
George Washington
Virginia
James Monroe
Virginia
Richard Nixon
California