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KENT lost two wickets in as many overs leading up to lunch, but continued their run-fest after the interval to reach 294 for two.
The visitors have lost only David Fulton (109) and Ed Smith for one on the third day of this Frizzell Championship clash against Northamptonshire.
Fulton featured in an excellent opening stand worth 222 with Rob Key (136 not out) and faced 226 balls for his second century of the summer.
The stand came to an end when, in attempting to sweep a full-length ball from Usman Afzaal, he dragged the ball onto his own stumps.
Smith got off the mark with a single, but fell in the very next over from former England one-day spinner Graeme Swann. Propping half forward, Smith sent a bat-pad catch to Tim Roberts at silly point.
Key and Symonds upped the tempo after the interval, Key reaching his third century in four innings while Symonds kept him company with an unbeaten 32.