Rules -- Circumnavi-Gates

Circumnavi-Gates was invented by the Japanese puzzle company Nikoli (under the name Suraromu).

1. Draw a single loop, starting and ending at the numbered circle. The loop may only travel horizontally or vertically, and never diagonally (so all turns are of 90 degrees). The loop may only turn at the centers of the grid cells. The loop may not cross itself or branch off. In other words, the interior of the loop will be a single polygon.
2. The dotted lines are called gates. The loop must pass straight through every gate exactly once, by traversing exactly one cell in each gate. (The number in the circle represents the total number of gates, and is included as a convenience.)
3. A numbered black cell represents the order in which the loop passes through the gate which touches that black cell. (If a numbered black cell is next to more than one gate, then the number refers only to the gate which has that same number on both ends.) A gate numbered 1 must be the first gate visited in the loop, starting from the circle and going in one of the two possible directions, a gate numbered 2 must be the second gate visited, and so forth. The other gates may be passed through in any order.

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