We have $m \geq 69$ ($m > 1$) lamps in a row, and each of them is either on or off. We modify the state of the lamps every $1$ second according to the following rule: if the $i$-th lamp and its neighbors (only one neighbor for $i = 1$ or $i = m$, otherwise two neighbors) are in the same state, then $i$-th lamp is switched off; otherwise, it is switched on. All the lamps are off except the leftmost initially.

Find all $m$ such that all of the lamps turn off after finite some time.