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Full or Half Sudoku (624)

Instruction:
Apply classic sudoku rules.
A circle marked at the intersection of a 2×2 block of cells indicates that numbers placed in these cells are either all odd or all even. A square marked at the intersection of a 2×2 block of cells indicates that exactly two numbers placed in these cells are odd, and exactly two numbers are even.

Reference: WPF (1)

Examples:
WPF Sudoku GP 2016 - Round 8 (104)
Parent puzzle:
Odd/Even Sudoku