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Curious Cheetah

Alternate Corners

Background

This is similar to Masyu, but has two key rule differences.
This puzzle appears in "Challenge Your Brain Math & Logic Puzzles" (Dave Tuller & Michael Rios, Puzzle Wright Press).

Puzzle and Goal

An unsolved puzzle consists of a rectangular grid; some cells contain white circles.
The goal is to draw a single open path that satisfies the clues.

Rules

The solved grid must satisfy the following conditions: