Fill in numbers from 1 to 6 in the blank cells in a way that there is no repetition of digits in any row

Please fill in numbers from 1 to 6 in the blank cells in a way that there is no repetition of digits in any row, column, or region; the numbers in gray cells are larger than those in adjacent white cells.

Starting with 1, F6=1 follows from the fact that all gray cells except for F6 are adjacent to white cells. E2=1 follows from the fortress rule for the 5th region. D1=1, A3=1, and B5=1 can be deduced through further eliminations.

Observing the 6th column, B6=2 follows from the fact that 2 must be greater than 1. C3=2 follows from the 3rd column. F5=6 cannot appear in any white cells adjacent to gray cells in the 5th column.

In the second region, A5 cannot be 5. If B4 is 5 then B3 must be 6, resulting in two 6’s in one region. Hence, A6=5. After eliminating F4 and E5 as possible 5’s, E4=5, and E3=6.

In the 3rd and 4th regions, C2 cannot be 5, and D5 must be 6 due to the gray cell next to the 5 in that region. C5=5, C6=6, D2=6, and D3=5 follow.

In the 3rd region, C1=4 and C2=3 follow from the fortress rule. C3=4 and F3=3 follow from further eliminations. B4=3 and F4=2 follow.

There are no more obstacles, so all the digits can be determined.