pnedulum clock gives corresct at the equator will it gain or loss the time as it is taken to the poles?

We know, Time period, T = 2π√{l/g}
where , l is length of simple pendulum, g is acceleration due to gravity.

we know, acceleration due to gravity, g value at pole is greater than at equator.

if it is taken to the poles g value increases. time period decreases so, the pendulum clock gains time.

hence, if a pendulum clock gives correct time at the equator then, it gains time if it is taken to the poles.