Let \(n\) be a positive integer \(\leq 1000.\) Suppose \(n\) bulbs are arranged in a row. Initially the first bulb is switched on and all other bulbs are switched off. Each second, we change the states of the bulbs according to the following rules:

If the state of a bulb is identical to the state of all its neighbors (one neighbor for the bulbs at the edges, two neighbors for the other bulbs), it is switched off.

Otherwise, it is switched on.

It turns out that eventually (after a finite amount of time) all bulbs are switched on. Find the largest possible value of \(n.\)

**Details and assumptions**

The state of a bulb refers to whether it is switched on or off.

This problem is inspired by ISL 2006 C1.

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