In the following grid, the numbers from 1 to 6 occur only once per row, per column, or per colored rectangle. Given the relations between numbers and a single number to get you started, can you complete the grid?
| | | | | | | | | | | | | |
| | > | | > | | | | < | | < | | | |
| v | | ^ | | v | | ^ | | ^ | | ^ | | |
| | < | | > | | | | > | | < | | | |
| | | | | | | | | | | | | |
| | < | | > | | | | < | | > | 3 | | |
| v | | v | | ^ | | ^ | | v | | ^ | | |
| | > | | < | | | | > | | < | | | |
| | | | | | | | | | | | | |
| | < | | < | | | | < | | > | | | |
| ^ | | v | | ^ | | v | | v | | ^ | | |
| | > | | < | | | | < | | > | | | |
| | | | | | | | | | | | | |