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An ant starts at the origin of the Cartesian coordinate plane. Each minute it moves randomly one unit in one of the directions up, down, left, or right, with all four directions being equally likely; its direction each minute is independent of its direction in any previous minutes. It stops when it reaches a point (x, y) such that |x| + |y| = 3. The expected number of moves it makes before stopping can be expressed as m/n for relatively prime positive integers m and n. Compute 100m + n