A staff is placed on a benchmark (BM) of reduced level (RL) $100.000 \: m$ and a theodolite is placed at a horizontal distance of $50 \: m$ from the BM to measure the vertical angles. The measured vertical angles from the horizontal at the staff readings of $0.400 \: m$ and $2.400 \: m$ are found to be the same. Taking the height of the instrument as $1.400 \: m$, the RL (in $m$) of the theodolite station is ____________