A pool has three water faucet and one drain faucet. The first water faucet can fill up the pool in $3$ hours, the second water faucet can fill up the pool in $4$ hours, and the third water faucet can fill up the pool in $6$ hours. However, the drain faucet can empty the pool in $12$ hours. How long will take to fill up the pool if the three faucet and the drain faucet are opened at the same time?