Ruth has a beaker containing a solution of $800$ mL of acid and $200$ mL of water. She thinks the solution is a little strong, so she drains $700$ mL from the beaker, adds $700$ mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains $400$ mL from the beaker, and adds $400$ mL of water. How many mL of water are now in the beaker?