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A sign is required to be put up asking drivers to slow down to $30$ km/h before entering Zone $Y$ (see figure). On this road, vehicles require $174$ m to slow down to $30$ km/h (the distance of $174$ m includes the distance travelled during the perception-reaction time of drivers). The sign can be read by $6/6$ vision drives from a distance of $48$ m. The sign is placed at a distance of $x$ m from the start of Zone $Y$ so that even a $6/9$ vision driver can slow down to $30$ km/h before entering the zone. The minimum value of $x$ is ________ m.

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