Find the largest integer \(N\) satisfying the following two conditions:

(i) \(\lfloor \frac N3 \rfloor\) consists of three equal digits;

(ii) \(\lfloor \frac N3 \rfloor = 1 + 2 + 3 +\cdots + n\) for some positive integer \(n.\)

\(\lfloor \cdot \rfloor\) denotes the floor function.

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